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Proceedings of the American Mathematical Society

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Mean growth and smoothness of analytic functions


Author: A. Matheson
Journal: Proc. Amer. Math. Soc. 85 (1982), 219-224
MSC: Primary 30D99; Secondary 46J15
DOI: https://doi.org/10.1090/S0002-9939-1982-0652446-3
MathSciNet review: 652446
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Abstract: Let $ {G_\alpha }$ denote the class of functions $ f(z)$ analytic in the unit disk such that

$\displaystyle \int_0^1 {{{(1 - r)}^{ - \alpha }}{M_\infty }(f',r)} dr < \infty ,$

for some $ \alpha (0 < \alpha < 1)$. A characterization of $ {G_\alpha }$ is given in terms of moduli of continuity and an application is given to Riesz factorization of functions in $ {G_\alpha }$.

References [Enhancements On Off] (What's this?)

  • [1] V. P. Havin, On the factorization of analytic functions smooth on the boundary, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 22 (1971), 202-205. MR 0289783 (44:6970)
  • [2] F. A. Šamojan, Division by an inner function in some spaces of functions analytic in the disk, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 22 (1971), 206-208. MR 0289786 (44:6973)
  • [3] A. Zygmund, Trigonometric series, Cambridge Univ. Press, London and New York, 1968. MR 0236587 (38:4882)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0652446-3
Article copyright: © Copyright 1982 American Mathematical Society

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