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Some questions on \(L^1\)-approximation in bergman spaces

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References

  1. Duren, P., Schuster, A.: Bergman Spaces, Mathematical Surveys and Monographs, vol. 100. American Mathematical Society, Providence, RI (2004). DOI: https://doi.org/10.1090/surv/100

  2. Duren, P.L.: Theory of \(H^{p}\) Spaces, Pure and Applied Mathematics, vol. 38. Academic Press, New York (1970)

    Google Scholar 

  3. Fisher, S.D.: Function Theory on Planar Domains. Pure and Applied Mathematics (New York). John Wiley & Sons, Inc., New York (1983). A second course in complex analysis, A Wiley-Interscience Publication

  4. Gamelin, T.W.: Uniform Algebras. Prentice-Hall Inc, Englewood Cliffs, N. J. (1969)

    MATH  Google Scholar 

  5. Garnett, J.B.: Bounded Analytic Functions. Pure and Applied Mathematics, vol. 96. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London (1981)

  6. Hoffman, K.: Banach Spaces of Analytic Functions. Prentice-Hall Series in Modern Analysis. Prentice-Hall Inc, Englewood Cliffs, N. J. (1962)

    Google Scholar 

  7. Kahane, J.P.: Best approximation in \(L^{1}(T)\). Bull. Am. Math. Soc. 80, 788–804 (1974). https://doi.org/10.1090/S0002-9904-1974-13518-4

    Article  MATH  Google Scholar 

  8. Khavinson, D.: Factorization theorems for different classes of analytic functions in multiply connected domains. Pacific J. Math. 108(2), 295–318 (1983). http://projecteuclid.org/euclid.pjm/1102720365

  9. Khavinson, D.: On removal of periods of conjugate functions in multiply connected domains. Michigan Math. J. 31(3), 371–379 (1984). https://doi.org/10.1307/mmj/1029003081

    Article  MathSciNet  MATH  Google Scholar 

  10. Khavinson, D., McCarthy, J.E., Shapiro, H.S.: Best approximation in the mean by analytic and harmonic functions. Indiana Univ. Math. J. 49(4), 1481–1513 (2000). https://doi.org/10.1512/iumj.2000.49.1787

    Article  MathSciNet  MATH  Google Scholar 

  11. Khavinson, D., Pérez-González, F., Shapiro, H.S.: Approximation in \(L^1\)-norm by elements of a uniform algebra. Constr. Approx. 14(3), 401–410 (1998). https://doi.org/10.1007/s003659900080

    Article  MathSciNet  MATH  Google Scholar 

  12. Khavinson, S.Y.: Foundations of the theory of extremal problems for bounded analytic functions and various generalizations of them. Am. Math. Soc. Transl. 2(129), 1–56 (1986)

    MATH  Google Scholar 

  13. Khavinson, S.Y.: Theory of factorization of single-valued analytic functions on compact Riemann surfaces with a boundary. Uspekhi Mat. Nauk 44(4(268)), 155–189, 256 (1989). DOI: https://doi.org/10.1070/RM1989v044n04ABEH002146

  14. Newman, D.J.: Pseudo-uniform convexity in \(H^{1}\). Proc. Am. Math. Soc. 14, 676–679 (1963). https://doi.org/10.2307/2034299

    Article  MATH  Google Scholar 

  15. Shapiro, H.S.: The Schwarz Function and its Generalization to Higher Dimensions. University of Arkansas Lecture Notes in the Mathematical Sciences, vol. 9. Wiley, New York (1992). A Wiley-Interscience Publication

  16. Totik, V.: Written communication (2019)

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Acknowledgements

The author gratefully acknowledges the support of the Simons Foundation. The author is indebted to the anonymous referee for suggestions that helped to improve the exposition.

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  1. Department of Mathematics & Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Dmitry Khavinson

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Khavinson, D. Some questions on \(L^1\)-approximation in bergman spaces. Complex Anal Synerg 7, 10 (2021). https://doi.org/10.1007/s40627-021-00072-1

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