Local smoothness of an analytic function compared to the smoothness of its modulus
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A. V. Vasin, S. V. Kislyakov and A. N. Medvedev
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 25 (2014), 397-420
- DOI: https://doi.org/10.1090/S1061-0022-2014-01296-4
- Published electronically: May 16, 2014
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Abstract:
Let $\Phi$ be a function analytic in the disk and continuous up to the boundary, and let its modulus of continuity satisfy the Hölder condition of order $\alpha$, $0<\alpha <2$, at a single boundary point. Under standard assumptions on the zeros of $\Phi$, this function must be then at least $\alpha /2$-Hölder (in a certain integral sense) at the same point. There are generalizations to not necessarily power-type Hölder smoothness.References
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Bibliographic Information
- A. V. Vasin
- Affiliation: State University of Maritime and Inland Shipping, ul. Dvinskaya 5/7, St. Petersburg 158035, Russia
- Email: andrejvasin@gmail.com
- S. V. Kislyakov
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: skis@pdmi.ras.ru
- A. N. Medvedev
- Affiliation: St. Petersburg State University, Universitetskii pr. 28, St. Petersburg 198504, Russia
- Email: alkomedvedev@gmail.com
- Received by editor(s): February 28, 2013
- Published electronically: May 16, 2014
- Additional Notes: Supported by RFBR (the first and the second authors), grant 11-01-00526
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 397-420
- MSC (2010): Primary 30H25
- DOI: https://doi.org/10.1090/S1061-0022-2014-01296-4
- MathSciNet review: 3184598
Dedicated: Dedicated to Boris Mikhaĭlovich Makarov