Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

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
Full-text PDF

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$.


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

  • 1. I. I. Privalov, Boundary properties of analytic functions, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950. (Russian) MR 0047765 (13:926h)
  • 2. K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Ser. Modern Analysis, Prentice Hall, Englewood Cliffs, NJ, 1962. MR 0133008 (24:A2844)
  • 3. A. Zygmund, Trigonometric series, Vol. I, Cambridge Univ. Press, Cambridge, 1959. MR 0107776 (21:6498)
  • 4. V. P. Havin and F. A. Šamojan, Analytic functions with a Lipschitzian modulus of the boundary values, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 19 (1970), 237-239. (Russian) MR 0289784 (44:6971)
  • 5. J. Brennan, Approximation in the mean by polynomials on non Caratheodory domains, Ark. Mat. 15 (1977), no. 1, 117-168. MR 0450566 (56:8859)
  • 6. N. A. Shirokov, Analytic functions smooth up to the boundary, Lecture Notes in Math., vol. 1312, Springer-Verlag, Berlin, 1988. MR 947146 (90h:30087)
  • 7. G. Ya. Bomash, Peak sets for analytic Holder classes, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 157 (1987), 129-136; English transl., J. Soviet Math. 44 (1989), no. 6, 837-842. MR 899281 (88f:46100)
  • 8. A. O. Gel'fond, The calculus of finite differences, Nauka, Moscow, 1967. (Russian) MR 0216186 (35:7021)
  • 9. J. B. Garnett, Bounded analytic functions, Pure and Appl. Math., vol. 96, Acad. Press, New York, 1981. MR 628971 (83g:30037)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 30H25

Retrieve articles in all journals with MSC (2010): 30H25


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

American Mathematical Society