Skip to main content
SpringerLink
Log in

Singular integrals, BMO, Hp

  • Chapter
  • First Online:
Linear and Complex Analysis Problem Book 3

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1573))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Khvedelidze B. V., The method of Cauchy type integrals in discontinuous boundary problems of the theory of holomorphic functions of one complex variable, Modern problems of mathematics 7 (1975), Moscow 5–162 (Russian); English transl. in J. Soviet Math.

    Google Scholar 

  2. Danilyuk I. I., Non-regular boundary problems on the plane, Nauka, Moscow, 1975 (Russian)

    Google Scholar 

  3. Duren P. L., Shapiro H. S., Shields A. L., Singular measures and domains not of Smirnov type, Duke Math. J. 33 (1966), no. 2, 247–254.

    Article  MathSciNet  MATH  Google Scholar 

  4. Tumarkin G. Ts., Boundary properties of analytic functions representable by a Cauchy type integral, Mat. Sb. 84(126) (1971), no. 3, 425–439 (Russian); English transl. in Math. USSR-Sb. 13 (1971). no. 3, 419–434.

    MathSciNet  MATH  Google Scholar 

  5. Paatashvili V. A., On singular integrals of Cauchy, Soobshch. Akad. Nauk Gruz. SSR, 53 (1969), no. 3, 529–532 (Russian)

    MathSciNet  Google Scholar 

  6. Dyn'kin e. M., On the uniform approximation by polynomials in the complex domain, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 56 (1975), 164–165 (Russian); English transl. in J. Soviet Math. 9 (1978), 269–271.

    Google Scholar 

  7. -, On the uniform approximation of functions on Jordan domains, Sibirsk. Mat. Zh. 18 (1977), no. 4, 775–786 (Russian); English transl. in Sib. Math. J. 18 (1978), 548–557.

    MathSciNet  Google Scholar 

  8. Andersson Jan-Erik, Ganelius Tord, The degree of approximation by rational function with fixed poles, Math. Z. 153 (1977), no. 2, 161–166.

    Article  MathSciNet  MATH  Google Scholar 

  9. Tumarkin G. Ts., Boundary properties of conformal mappings of certain classes of domains, In: Some questions of modern function theory, Novosibirsk, 1976, pp. 149–160. (Russian).

    Google Scholar 

  10. Ahlfors L., Lectures on quasiconformal mappings, Van Nostrand Reinhold, 1966.

    Google Scholar 

  11. Havin V. P., Boundary properties of Cauchy type integrals and harmonic conjugate functions in domains with rectifiable boundaries, Mat. Sb. 68(110) (1965), 499–517 (Russian); English transl. in Amer. Math. Soc. Transl. 74 (1968), no. 2, 40–60.

    MathSciNet  Google Scholar 

  12. Belyi V. I., Miklyukov V. M., Some properties of conformal and quasiconformal mappings, and direct theorems of the constructive function theory, Izv. Akad. Nauk SSSR Ser. Mat. (1974), no. 6, 1343–1361 (Russian); English transl. in Math. USSR Izv. 8 (1974).

    Google Scholar 

  13. Belyi V. I., Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary, Mat. Sb. 102 (1977), no. 3, 331–361 (Russian); English transl., in Math. USSR-Sb. 31 (1977), no. 3, 289–317.

    MathSciNet  MATH  Google Scholar 

References

  1. David G., Opérateurs intégraux singuliérs sur certaines courbes du plan complexe, Ann. Sci. E.N.S. 17 (1984), no. 1, 157–189.

    MATH  Google Scholar 

Reference

  1. Coifman R. R., McIntosh A., Meyer Y. L'intégrale de Cauchy définit un opérateur borné sur L 2 pour les courbes Lipschitziennes, Ann. Math. 116 (1982), 361–387.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Astala K.; Calderón's problem for Lipschitz classes and the dimension of quasicircles, Revista Matemática Iberoamericana 4 (1988), 469–486.

    Article  MathSciNet  MATH  Google Scholar 

  2. Dont M., Non-tangent limits of the double layer potentials, Časopis pro pêstování matematiky 97 (1972), 231–258.

    MathSciNet  MATH  Google Scholar 

  3. Král J., Lukeš J., Integrals of the Cauchy type, Czechoslovak Math. J. 22 (1972), 663–682.

    MathSciNet  MATH  Google Scholar 

  4. Král J., Integral operators in Potential theory, Lecture Notes in Math., vol. 823, Springer-Verlag, 1980.

    Google Scholar 

  5. Saks S., Theory of the integral, Dover Pub. 1964.

    Google Scholar 

References

  1. David G., Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. 17 (1984), 157–189.

    MATH  Google Scholar 

  2. Krzyż J. G., Generalized Neumann-Poincaré operator and chord-arc curves, Ann. Univ. M. Curie-Skłodowska Sect. A 43 (1989), 69–78.

    MATH  Google Scholar 

  3. Zinsmeister M., Domaines de Lavrentiev, Publ. Math. d'Orsay, Paris 1985.

    MATH  Google Scholar 

References

  1. Cotlar M., Sadosky C., On some L p versions of the Helson-Szegö theorem, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth, Belmont, California, 1983, pp. 306–317.

    Google Scholar 

  2. Jurkat W. B., Sampson G., On rearrangement and weight inequalities for the Fourier transform, Indiana Univ. Math. J. 33 (1984), no. 2, 257–270.

    Article  MathSciNet  MATH  Google Scholar 

  3. Muckenhoupt B., Weighted norm inequalities for classical operators, Proc. Symp. in Pure Math. 35 (1979), no. 1, 69–83.

    Article  MathSciNet  MATH  Google Scholar 

  4. Muckenhoupt, B., Weighted norm inequalities for the Fourier transform, Trans. Amer. Math. Soc. 276 (1983), 729–742.

    Article  MathSciNet  MATH  Google Scholar 

  5. Sawyer E., Two weight norm inequalities for certain maximal and integral operators, Harmonic Analysis, Lecture Notes in Math., vol. 908 Springer, Berlin, 1982, pp. 102–127.

    MATH  Google Scholar 

  6. Sawyer E., Norm inequalities relating singular integrals and the maximal function, Studia Math. 75 (1983), no. 3, 253–263.

    MathSciNet  MATH  Google Scholar 

  7. Sawyer E., Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator, Trans. Amer. Math. Soc. 281 (1984), no. 1, 329–337.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Gohberg I. Ts., Krupnik N. Ya., Norm of the Hilbert transformation in the space L p, Funktsional. Anal. i Prilozhen. 2 (1968), no. 2, 91–92 (Russian); English transl. in Functional. Anal. Appl. 2 (1968), no. 2, 180–181.

    Google Scholar 

  2. Pichorides S. K., On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), no. 2, 165–179.

    MathSciNet  MATH  Google Scholar 

  3. Krupnik N. Ya., Polonskii E. P., On the norm of an operator of singular integration, Funktsional. Anal. i Prilozhen. 9 (1975), no. 4, 73–74 (Russian); English transl. in Finctional. Anal. Appl. 9 (1975), no. 4, 337–339.

    MathSciNet  Google Scholar 

  4. Verbitsky I. È., Estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary parts, In: Matem. issledovaniya, Shtiintsa, Kishinev, 1980, pp. 16–20. (Russian)

    Google Scholar 

  5. Verbitsky I. È., Krupnik N. Ya., Sharp constants in the theorems of K. I. Babenko and B. V. Khvedelidze on the boundedness of a singular operator, Soobshch. Akad. Nauk Gruz. SSR 85 (1977), no. 1, 21–24. (Russian)

    Google Scholar 

  6. Gohberg I. C., Krupnik N. Ya., Einführung in die Theorie der eindimensionalen singulären Integraloperatoren, Birkhäuser Verlag, 1979 (transl. from Russian).

    Google Scholar 

  7. Nikol'skii N. K., Treatise on the Shift Operator, Springer-Verlag 1986 (transl. from Russian).

    Google Scholar 

  8. Hardy G. H., Littlewood J. E., Pólya G., Inequalities, 2nd ed., Cambridge Univ. Press, London and New York, 1952.

    MATH  Google Scholar 

References

  1. David G., Courbes corde-arc et espaces de Hardy généralisés, Ann. Inst. Fourier (Grenoble) 32 (1982), 227–239.

    Article  MathSciNet  MATH  Google Scholar 

  2. Garnett J., O'Farell A., Sobolev approximation by a sum of subalgebras on the circle, Pacific J. Math. 65 (1976), 55–63.

    Article  MathSciNet  MATH  Google Scholar 

  3. Jones P., Homeomorphisms of the line which preserve BMO, Ark. Mat. 21 (1983), no. 2, 229–231.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Moore C. N., Some Applications of Cauchy Integrals on Curves, University of California, Los Angeles, 1986.

    Google Scholar 

  2. Bishop C. J., A counterexample in conformal welding concerning Hausdorff dimension, Michigan Math. J. 35 (1988), 151–159.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Arocena R., A refinement of the Helson-Szegö theorem and the determination of the extremal measures, Studia Math. LXXI (1981), 203–221.

    MathSciNet  MATH  Google Scholar 

  2. Coifman R., Rochberg R., Projections in weighted spaces, skew projections, and inversion of Toeplitz operators, Integral Equations and Operator Theory 5 (1982), 145–159.

    Article  MathSciNet  MATH  Google Scholar 

  3. Coifman R., Rochberg R., Weiss G., Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Uchiyama A., A constructive proof of the Fefferman-Stein decomposition of BMO(ℝn), Acta Math. 148 (1982), 215–241.

    Article  MathSciNet  MATH  Google Scholar 

  2. Uchiyama A., The Fefferman-Stein decomposition of smooth functions and its application to H p(ℝn), University of Chicago, Ph.D. thesis, 1982.

    Google Scholar 

  3. Calderón, A. P., Zygmund A., On higher gradients of harmonic functions, Studia Math. 24 (1964), 211–226.

    MathSciNet  MATH  Google Scholar 

References

  1. Fefferman C., Stein E. M., H p spaces of several variables, Acta Math. 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  2. Stein E. M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.

    Google Scholar 

  3. Wolff T., Couterexamples with harmonic gradient in ℝ3, preprint.

    Google Scholar 

  4. Aleksandrov A. B., Kargaev P. P., Hardy classes of functions harmonic in the half-space, Algebra i Analiz 5 (1993), no. 2, 1–70. (Russian)

    MathSciNet  MATH  Google Scholar 

  5. Aleksandrov A. B., Essays on non locally convex Hardy classes. Lect. Notes Math. 864 (1981), 1–89.

    Article  MATH  Google Scholar 

  6. Aleksandrov A. B., Approximation by rational functions and an analog of the M. Riesz theorem on conjugate functions for L p-spaces with p∈(0, 1), Matem. Sbornik 107(149) (1978), no. 1(9), 3–19 (Russian); English transl. in Math. USSR— Sbornik 35 (1979), 301–316.

    Google Scholar 

  7. Stein E. M., Weiss G., Generalization of the Cauchy-Riemann equations and representation of the rotation group, Amer. Math. J. 90 (1968), 163–196.

    Article  MathSciNet  MATH  Google Scholar 

  8. Alekseev R. B., On a subharmonic property of solutions of generalized Cauchy-Riemann equations, Vestnik LGU (to appear). (Russian)

    Google Scholar 

  9. Garnett J. B. Bounded Analytic Functions, Academic Press, 1981.

    Google Scholar 

References

  1. [M] Müller P. F. X., Permutations of the Haar system, in GAFA Seminar (V. Milman & J. Lindenstrauss, eds.), Lect. Notes Math., vol. 1469, Springer-Verlag, 1991, pp. 125–126.

    Google Scholar 

  2. [S] Schipp F., On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces, Analytic Mathematica 16 (1990), 135–143.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Kisliakov S. V., Fourier coefficients of boundary values of functions analytic in the disc and in the bidisc, Trudy Mat. Inst. Steklov 155 (1981), 77–94 (Russian); English transl. in Proc. Steklov Inst. Math. 155 (1983), 75–92.

    MathSciNet  Google Scholar 

  2. Bourgain J., Extensions of H ∞-valued functions and bounded bianalytic functions, preprint, 1982.

    Google Scholar 

Reference

  1. Sjögren P., Translation-invariant operators on weak L 1, J. Funct. Anal. 89 (1990), 410–427.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Marshall D., Blaschke products generate H ∞, Bull. Amer. Math. Soc. 82 (1976), 494–496.

    Article  MathSciNet  MATH  Google Scholar 

  2. Marshall D., Subalgebras of L ∞ containing H ∞, Acta Math. 137 (1976), 91–98.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hunt R. A., Muckenhoupt B., Wheeden R. L., Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227–251.

    Article  MathSciNet  MATH  Google Scholar 

  4. Helson H., Szegö G., A problem in prediction theory, Ann. Math. Pure Appl. 51 (1960), 107–138.

    Article  MathSciNet  MATH  Google Scholar 

  5. Fefferman C., Stein E. M., H p spaces of several variables, Acta Math. 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  6. Carleson L., Two remarks on H 1 and BMO, Advances in Math. 22 (1976), 269–277.

    Article  MathSciNet  MATH  Google Scholar 

  7. Stein E. M., Singular integrals and differentiability properties of functions, Princeton N. J., 1970.

    Google Scholar 

  8. Janson S., Characterization of H 1 by singular integral transforms on martingales and ℝn, Math. Scand. 41 (1977), 140–152.

    MathSciNet  Google Scholar 

References

  1. Wolff T., Counterexamples to two variants of the Helson-Szegö theorem, preprint, vol. 11, Institut Mittag-Leffler, 1983.

    Google Scholar 

  2. Jones P., Carleson measures and the Feffermann-Stein decomposition of BMO(ℝ), Ann. of Math. 111 (1980), 197–208.

    Article  MathSciNet  Google Scholar 

  3. Jones P., L ∞-estimates for the -problem in a half-plane, Acta Math. 150 (1983), no. 1-2, 137–152.

    Article  MathSciNet  MATH  Google Scholar 

  4. Uchiyama A., A constructive proof of the Fefferman-Stein decompositions of BMO(ℝn), Acta Math. 148 (1982), 215–241.

    Article  MathSciNet  MATH  Google Scholar 

  5. Stray A., Two applications of the Schur-Nevanlinna algorithm, Pacif. J. of Math. 91 (1980), no. 1, 223–232.

    Article  MathSciNet  MATH  Google Scholar 

  6. Rubio de Francia J. L., Factorization and extrapolation by weights, Bull. Amer. Math. Soc. 7 (1982), no. 2, 393–395.

    Article  MathSciNet  MATH  Google Scholar 

  7. Amar E., Représentation des fonctions de BMO et solutions de l'équation , preprint, Univ. Paris XI Orsay, 1978.

    Google Scholar 

  8. Coifman R., Jones P. W., Rubio de Francia J. L., Constructive decomposition of BMO functions and factorization of A p weights, Proc. Amer. Math. Soc. 87 (1983), no. 4, 675–680.

    MathSciNet  MATH  Google Scholar 

  9. Marshall D., Stray A., Interpolating Blaschke products, Pacif. J. Math. (to appear).

    Google Scholar 

References

  1. Baernstein A. H., Univalence and bounded mean oscillation, Mich. Math. J. 23 (1976), 217–223.

    Article  MathSciNet  MATH  Google Scholar 

  2. Helson H., Szegö G., A problem in prediction theory, Ann. Mat. Pura Appl. 51 (1960), no. 4, 107–138.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hunt R., Muckenhoupt B., Wheeden R., Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227–251.

    Article  MathSciNet  MATH  Google Scholar 

  4. Fefferman C., Stein E. M., H p spaces of several variables, Acta Math. 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  5. Baernstein A. H., Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), 139–169.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Zygmund A., Trigonometric Series, vol. I, Cambridge Univ. Press, Cambridge, 1959.

    MATH  Google Scholar 

  2. Anderson J. M., Clunie J., Pommerenke Ch., On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12–37.

    MathSciNet  MATH  Google Scholar 

  3. Pommerenke Ch., On univalent functions, Bloch functions and VMOA, Math. Ann. 236 (1978), no. 3, 199–208.

    Article  MathSciNet  MATH  Google Scholar 

  4. Sarason D., Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391–405.

    Article  MathSciNet  MATH  Google Scholar 

  5. Shapiro H. S., Monotonic singular functions of high smoothness, Michigan Math. J. 15 (1968), 265–275.

    Article  MathSciNet  MATH  Google Scholar 

  6. Kahane J.-P., Trois notes sur les ensembles parfaits linéaires, Enseignement Math. 15 (1969), no. 2, 185–192.

    MathSciNet  Google Scholar 

References

  1. Bishop C. J., Bounded functions in the little Bloch spaces, Pacific J. Math. 142 (1990), 209–225.

    Article  MathSciNet  MATH  Google Scholar 

  2. Cochran W. G., Random Blaschke products, Trans. Amer. Math. Soc. 322 (1990), 731–755.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hungerford G. J., boundaries of smooth sets and singular sets of Blaschke products in the little Bloch class, Thesis, California Institute of Technology, Pasadena, California, 1988.

    Google Scholar 

References

  1. Chang S.-Y. A., Marshall D., A sharp inequality concerning the Dirichlet integral, Am. J. Math. 107 (1985), no. 5, 1015–1034.

    Article  MathSciNet  MATH  Google Scholar 

  2. Moser J., A sharp form of an inequality by N. Trudinger, Ind. Univ. Math. J. 20 (1971), 1077–1092.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Sarason D., Algebras between L ∞ and H ∞, Lect. Notes in Math., Springer-Verlag 512 (1976), 117–129.

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang S.-Y. A., Structure of some subalgebra of L ∞ of the torus, Proc. Symposia in Pure Math. 35, Part 1 (1979), 421–426.

    Article  MathSciNet  Google Scholar 

Reference

  1. Ahern P., The mean modulus and the derivative of an inner function, Indiana Univ. Math. J. 28 (1979), no. 2, 311–347.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Dyakonov K. M., Smooth functions and coinvariant subspaces of the shift operator, Algebra i Analiz 4 (1992), no. 5, 117–147 (Russian); English transl. in St. Petersburg Math. J. 4 (1993), no. 5.

    MathSciNet  Google Scholar 

  2. Garnett J. B., Bounded Analytic Functions, Academic Press, NY, 1981.

    MATH  Google Scholar 

References

  1. Parreau, M., Théorème de Fatou et problème de Dirichlet pour les lignes de Green de certaines surfaces de Riemann, Ann. Acad. Sci. Fenn. Ser. A. I, Math. (1958), no. 250/25, 8 pp.

    Google Scholar 

  2. Widom, H., H p sections of vector bundles over Riemann surfaces, Ann. of Math. 94 (1971), 304–324.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hasumi, M., Hardy Classes on Infinitely Connected Riemann surfaces, Lecture Notes in Mathematics, Vol. 1027 Springer-Verlag, 1983.

    Google Scholar 

  4. Brelot, M., Topology of R. S. Martin and Green lines, Lectures on Functions of a Complex Variable, Univ. of Michigan Press, Ann Arbor, 1955, pp. 105–121.

    MATH  Google Scholar 

  5. Hayashi, M., Invariant subspaces on Riemann surfaces of Parreau-Widom type, Trans. Amer. Math. Soc., 279 (1983), 737–757.

    Article  MathSciNet  MATH  Google Scholar 

  6. Nakai, M., Corona problems for Riemann surfaces of Parreau-Widom type. Pacific J. Math. 103 (1982), 103–109.

    Article  MathSciNet  MATH  Google Scholar 

  7. Voichick, M., Extreme points of bounded analytic functions on infinitely connected regions, Proc. Amer. Math. Soc., 17 (1966), 1366–1369.

    MathSciNet  MATH  Google Scholar 

  8. Neville, C., Invariant subspaces of Hardy classes on infinitely connected open surfaces, Memoirs of the Amer. Math. Soc. No. 160, 1975.

    Google Scholar 

Reference

  1. Casazza P. G., Pengra R., Sundberg C., Complemented ideals in the disk algebra, Israel J. Math. 37 (1980), no. 1-2, 76–83.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Ahern P., Rudin W., Factorizations of bounded holomorphic functions, Duke Math. J. 39 (1972), 767–777.

    Article  MathSciNet  MATH  Google Scholar 

  2. Forelli, F., Two-sheeted coverings of the disc, Math. Scand. 61 (1987) 17–38.

    MathSciNet  MATH  Google Scholar 

References

  1. Dyakonov K. M., Division and multiplication by inner functions and embedding theorems for starinvariant subspaces, Amer. J. Math. (to appear).

    Google Scholar 

  2. Dynaknov K. M., Invariant subspaces of the backward shift operator in Hardy spaces, Thesis, St. Petersburg State University, St. Petersburg, 1991. (Russian)

    Google Scholar 

  3. Shirokov N. A., Ideals and factorization in algebras of analytic functions smooth up to the boundary Tr. Mat. Inst. Steklova 130 (1978), 196–222 (Russian)

    MathSciNet  MATH  Google Scholar 

  4. Shirokov N. A., Division and multiplication by inner functions in spaces of analytic functions smooth up to the boundary, Lect. Notes in Math., vol. 864, 1981, pp. 413–439.

    Article  MathSciNet  MATH  Google Scholar 

  5. Shirokov N. A., Analytic functions smooth up to the boundary, Lect. Notes in Math., vol. 1312, 1988.

    Google Scholar 

  6. Garnett J. B., Bounded Analytic Functions, Academic Press, New York, 1981.

    MATH  Google Scholar 

  7. Janson S., On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189–196.

    Article  MathSciNet  MATH  Google Scholar 

  8. Stegenga D. A., Bounded Toeplitz operators on H 1 and applications of the duality between H 1 and the functions of bounded mean oscillation, Amer. J. Math. 98 (1976), 573–589.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Anderson J. M., Clunie J., Pommerenke Ch., On Block functions and normal functions, J. Reine Angew. Math. 270 (1974), 12–37.

    MathSciNet  MATH  Google Scholar 

  2. Pommerenke Ch., Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation. Comment. Math. Helv. 52 (1977), 591–602.

    Article  MathSciNet  MATH  Google Scholar 

  3. Anderson J. M., On division by inner factors, Comment. Math. Helv. 54 (1979), no. 2, 309–317.

    Article  MathSciNet  MATH  Google Scholar 

  4. Havin V. P., On the factorization of analytic functions smooth up to the boundary, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 22 (1971), 202–205 (Russian)

    MathSciNet  Google Scholar 

  5. Gurarii V. P., On the factorization of absolutely convergent Taylor series and Fourier integrals, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 30 (1972), 15–32. (Russian).

    MathSciNet  Google Scholar 

References

  1. Gorkin P., Prime ideals in closed subalgebras of L ∞, Michigan Math. J. 33 (1986), 315–323.

    Article  MathSciNet  MATH  Google Scholar 

  2. Gorkin P., Hedenmalm H., Mortini R., A Beurling-Rudin theorem for H ∗, Illinois Math. J. 31 (1987), 629–644.

    MathSciNet  MATH  Google Scholar 

  3. Dyakonov K. M., Division and multiplication by inner functions and embedding theorems for starinvariant subspaces, Amer. J. Math. (to appear).

    Google Scholar 

  4. Mortini R., Gorkin P., F-ideals in QA B J. London Math. Soc. 37 (1988), 509–519.

    MathSciNet  MATH  Google Scholar 

  5. Hedenmalm H., On the f-and K-properties of certain function spaces, Contemporary Mathematics 91 (1989), 89–91.

    Article  MathSciNet  MATH  Google Scholar 

  6. Izuchi K., VMO has the K-property, preprint.

    Google Scholar 

  7. Wolff T., Two algebras of bounded functions, Duke Math. J. 49 (1982), 321–328.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Fefferman C., Stein E. M., H p spaces of several variables, Acta Math. 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

Reference

  1. A. Uchiyama, On the radial maximal function of distributions, Pacific J. of Math. 121 (1986), 467–483.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Technion, 32000, Haifa, Israel

    E. M. Dyn'kin

  2. St. Petersburg branch of Steklov Mathematical Institute Fontanka 27, 191011, St. Petersburg, Russia

    S. V. Kisliakov

Authors
  1. E. M. Dyn'kin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. V. Kisliakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Victor P. Havin Nikolai K. Nikolski

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this chapter

Cite this chapter

Dyn'kin, E.M., Kisliakov, S.V. (1994). Singular integrals, BMO, Hp . In: Havin, V.P., Nikolski, N.K. (eds) Linear and Complex Analysis Problem Book 3. Lecture Notes in Mathematics, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100211

Download citation

  • DOI: https://doi.org/10.1007/BFb0100211

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57870-3

  • Online ISBN: 978-3-540-48367-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation