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Hardy Spaces of Analytic Functions

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Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces

Part of the book series: RSME Springer Series ((RSME,volume 2))

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Abstract

In this chapter we give a short presentation of Hardy spaces.

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References

  1. Duren, P.L.: Theory of \(H^p\) Spaces (Academic Press, New York 1970; reprinted with supplement by Dover Publications. Mineola, NY 2000)

    Google Scholar 

  2. Garnett, J.B.: Bounded Analytic Functions. Academic Press, New York (1981)

    MATH  Google Scholar 

  3. Koosis, P.: Introduction to \(H_p\) Spaces, 2nd edn. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  4. Zhu, K.: Operator Theory in Function Spaces, Second edition, Mathematical Surveys and Monographs, vol. 138. American Mathematical Society, Providence (2007)

    Book  Google Scholar 

  5. Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. Springer, New York (2005)

    MATH  Google Scholar 

  6. Pavlović, M.: Introduction to Function Spaces on the Disk. Matematički Institut Sanu, Belgrade (2004)

    MATH  Google Scholar 

  7. Pavlović, M.: Function Classes on the Unit Disc. An Introduction, De Gruyter Studies in Mathematics 52, Berlin (2014)

    Google Scholar 

  8. Hollenbeck, B., Verbitsky, I.: Best constants for the Riesz projection. J. Funct. Anal. 175, 370–392 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gohberg, I., Krupnik, N.: Norm of the Hilbert transformation in the \(L_p\) space. Funct. Anal. Pril. 2, 91–92 (1968) (in Russian); English transl. in Funct. Anal. Appl. 2, 180–181 (1968)

    Google Scholar 

  10. Mateljević, M., Pavlović, M.: \(L^p\)-behavior of power series with positive coefficients and Hardy spaces. Proc. Am. Math. Soc. 87, 309–316 (1983)

    MathSciNet  MATH  Google Scholar 

  11. Hardy, G.H., Littlewood, J.E.: Some properties of fractional integrals, II. Math. Z. 34, 403–439 (1932)

    Article  MathSciNet  MATH  Google Scholar 

  12. Shields, A.L., Williams, D.L.: Bounded projections and the growth of harmonic conjugates in the unit disk. Mich. Math. J. 29, 3–25 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. Burkholder, D.L., Gundy, R.F., Silverstein, M.L.: A maximal function characterization of the class \(H^p\). Trans. Am. Math. Soc. 157, 137–153 (1971)

    MathSciNet  MATH  Google Scholar 

  14. Pavlović, M.: On harmonic conjugates with exponential mean growth. Czech. Math. J. 49(124), 733–742 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kislyakov, S.V., Xu, Q.: Real interpolation and singular integrals. St. Petersbg. Math. J. 8, 593–615 (1996)

    MathSciNet  MATH  Google Scholar 

  16. Zygmund, A.: Trigonometric Series, 2nd edn., Vols. I and II. Cambridge University Press, London (1968)

    Google Scholar 

  17. Beurling, A.: On two problems concerning linear transformations in Hilbert space. Acta Math. 81, 239–255 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pavlović, M.: Mean values of harmonic conjugates in the unit disk. Complex Var. Theory Appl. 10, 53–65 (1988)

    Article  MATH  Google Scholar 

  19. Bourgain, J.: New Banach space properties of the disc algebra and \(H^{\infty }\). Acta Math. 152, 1–48 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hardy, G.H., Littlewood, J.E.: Notes on the theory of series (XX). Generalizations of a theorem of Paley. Q. J. Math. Oxf. Ser. 8, 161–171 (1937)

    Google Scholar 

  21. Jevtić, M., Pavlović, M.: Littlewood-Paley type inequalities for \(M\)-harmonic functions. Publications de l’Institute mathematique 64(78), 36–52 (1998)

    Google Scholar 

  22. Tomaszewski, B.: The best constant in a weak-type \(H^1\)-inequality. Complex Var. Theory Appl. 4, 35–38 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  23. Djordjević, O., Pavlović, M.: On a Littlewood-Paley type inequality. Proc. Am. Math. Soc. 135(11), 3607–3611 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pavlović, M.: A short proof of an inequality of Littlewood and Paley. Proc. Am. Math. Soc. 134(12), 3625–3627 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pavlović, M.: Characterizations of the harmonic Hardy space \(h^1\) on the real ball. Filomat (Niš) 25, 137–143 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kalaj, D., Meštrović, R.: Isoperimetric type inequalities for harmonic functions. J. Math. Anal. Appl. 373(2), 439–448 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Duren, P.L., Schuster, A.P.: Bergman Spaces, Mathematical Surveys and Monographs 100. American Mathematical Society, Providence (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Miroljub Jevtić

  2. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain

    Dragan Vukotić

  3. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Miloš Arsenović

Authors
  1. Miroljub Jevtić
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  2. Dragan Vukotić
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  3. Miloš Arsenović
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Correspondence to Miroljub Jevtić .

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Jevtić, M., Vukotić, D., Arsenović, M. (2016). Hardy Spaces of Analytic Functions. In: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. RSME Springer Series, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-45644-7_4

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