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Sufficient conditions for the Hölder smoothness of a function


Author: N. A. Shirokov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 25 (2013), nomer 3.
Journal: St. Petersburg Math. J. 25 (2014), 507-511
MSC (2010): Primary 30H25
DOI: https://doi.org/10.1090/S1061-0022-2014-01302-7
Published electronically: May 16, 2014
MathSciNet review: 3184604
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Abstract | References | Similar Articles | Additional Information

Abstract: An outer function in the unit disk satisfies the Hölder condition of order $ ps/(p+1)$ provided its modulus is $ s$-Hölder on the unit circle and has logarithm in $ L^p$.


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  • 1. I. I. Privalov, Graničnye svoĭstva analitičeskih funkciĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950 (Russian). 2d ed.]. MR 0047765
  • 2. Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
  • 3. A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
  • 4. V. P. Havin and F. A. Šamojan, Analytic functions with a Lipschitzian modulus of the boundary values., Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 19 (1970), 237–239 (Russian). MR 0289784
  • 5. James E. Brennan, Approximation in the mean by polynomials on non-Carathéodory domains, Ark. Mat. 15 (1977), no. 1, 117–168. MR 0450566, https://doi.org/10.1007/BF02386037
  • 6. Nikolai A. Shirokov, Analytic functions smooth up to the boundary, Lecture Notes in Mathematics, vol. 1312, Springer-Verlag, Berlin, 1988. MR 947146
  • 7. G. Ya. Bomash, Peak sets for analytic Hölder classes, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 157 (1987), no. Issled. po Lineĭn. Operator. i Teorii Funktsiĭ. XVI, 129–136, 181–182 (Russian, with English summary); English transl., J. Soviet Math. 44 (1989), no. 6, 837–842. MR 899281, https://doi.org/10.1007/BF01463192
  • 8. A. O. Gel′fond, \cyr Ischislenie konechnykh raznosteĭ, Third corrected edition, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0216186
  • 9. John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971

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Additional Information

N. A. Shirokov
Affiliation: Department of mathematics and mechanics, St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg 198504, Russia
Email: nikolai.shirokov@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2014-01302-7
Keywords: H\"older classes, outer function
Received by editor(s): February 15, 2013
Published electronically: May 16, 2014
Dedicated: To dear Boris Mikhaĭlovich Makarov, with great respect
Article copyright: © Copyright 2014 American Mathematical Society