Mean growth and smoothness of analytic functions
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- by A. Matheson PDF
- Proc. Amer. Math. Soc. 85 (1982), 219-224 Request permission
Abstract:
Let ${G_\alpha }$ denote the class of functions $f(z)$ analytic in the unit disk such that \[ \int _0^1 {{{(1 - r)}^{ - \alpha }}{M_\infty }(f’,r)} dr < \infty ,\] 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
- V. P. Havin, The factorization of analytic functions that are smooth up to the boundary, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 22 (1971), 202–205 (Russian). MR 0289783
- F. A. Šamojan, Division by an inner function in certain spaces of functions that are analytic in the disc, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 22 (1971), 206–208 (Russian). MR 0289786
- A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Additional Information
- © Copyright 1982 American Mathematical Society
- 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