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Counterexamples to two variants of the Helson-Szegö theorem

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Baernstein,Some sharp inequalities for conjugate functions, Indiana Univ. Math. J.27 (1978), 833–852.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Baernstein,Analytic functions of bounded mean oscillation, inAspects of Contemporary Complex Analysis (D. A. Brannan and J. G. Clunie, eds.), Academic Press, New York, 1980.

    Google Scholar 

  4. R. Coifman and C. Fefferman,Weighted norm inequalities for maximal functions and singular integrals, Studia Math.51 (1974), 241–250.

    MATH  MathSciNet  Google Scholar 

  5. R. Douglas,Banach Algebra Techniques in the Theory of Toeplitz Operators, AMS Regional Conference Series in Mathematics, No. 15, 1973.

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

    MATH  Google Scholar 

  7. J. Gamett and P. Jones,The distance in BMO to L ∞, Ann. of Math.108 (1978), 373–393.

    Article  MathSciNet  Google Scholar 

  8. H. Helson and G. Szegö,A problem in prediction theory, Ann. Mat. Pura Appl.51 (1960), 107–138.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Jerison,The failure of L p estimates for harmonic measure in chord-arc domains, Abstract No. 797-30-17, Amer. Math. Soc. Abstracts3, No. 6, p. 425 (1982); preprint 1982.

    Google Scholar 

  11. D. Jerison and C. Kenig,Hardy spaces, A ∞ and singular integrals on chord-arc domains, Math. Scand.50 (1982), 221–248.

    MATH  MathSciNet  Google Scholar 

  12. P. Jones,Estimates for the corona problem, J. Funct. Anal.39 (1980), 162–181.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Jones and M. Zinsmeister,Sur la transformation conforme des domaines de Lavrentiev, C. R. Acad. Sci. Paris295 (1982), 563–566.

    MATH  MathSciNet  Google Scholar 

  14. Y. Katznelson,An Introduction to Harmonic Analysis, Dover, New York, 1976.

    MATH  Google Scholar 

  15. P. Koosis,Lectures on H p Spaces, London Math. Soc. Lecture Note Ser.40, Cambridge University Press, 1980.

  16. G. Sansone and J. Gerretsen,Lectures on the Theory of Functions of a Complex Variable, Vol. 2, Wolters-Noordhoff, Gronigen, 1969.

    MATH  Google Scholar 

  17. D. Sarason,Function theory on the unit circle, Virginia Polytechnic Institute and State Univ., Blacksburg, VA, 1979.

    Google Scholar 

  18. E. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1971.

  19. V. A. Tolokonnikov,Estimates in the Carleson corona theorem, ideals of the algebra H ∞,a problem of Sz.-Nagy, Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov. (LOMI)113 (1981), 178–198.

    MathSciNet  Google Scholar 

  20. M. Zinsmeister,Courbes de Jordan vérifiant une condition corde-arc, Ann. Inst. Fourier (Grenoble)32 (1982), 13–21.

    MATH  MathSciNet  Google Scholar 

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Authors
  1. Thomas H. Wolff
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Additional information

Tom Wolff wrote this paper in 1983 but never plublished it With the permission of Tom’s family, I have edited the paper for publication here. The mathematics is exactly as it was in Tom’s 1983 manuscript; only stylistic changes have been made. Preparation of the manuscript was supported by NSF Grant DMS-0070782.

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Wolff, T.H. Counterexamples to two variants of the Helson-Szegö theorem. J. Anal. Math. 88, 41–62 (2002). https://doi.org/10.1007/BF02786574

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