Real Analysis Exchange

Fourier Coefficients and Generalized Lipschitz Classes

S. S. Volosivets

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In this paper we give some equivalence relations between behavior of Fourier coefficients of a special kind and smoothness of functions. A necessary and sufficient condition for existence of Schwartz derivative is also obtained.

Article information

Real Anal. Exchange, Volume 34, Number 1 (2008), 219-226.

First available in Project Euclid: 19 May 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A10: Trigonometric approximation
Secondary: 41A25: Rate of convergence, degree of approximation

absolute convergence moduli of smoothness generalized Lipschitz classes


Volosivets, S. S. Fourier Coefficients and Generalized Lipschitz Classes. Real Anal. Exchange 34 (2008), no. 1, 219--226.

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