This article is cited in 4 papers

Sine and cosine series in $L_\varphi$ classes

B. V. Simonov

Chair of Applied Mathematics, Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005 Russia

Abstract: We study sine and cosine series with monotone with respect to subsequences coefficients. We establish conditions under which their sums belong to classes $L_\varphi$.

Keywords: monotonicity, series, subsequence, coefficients.

UDC: 517.518

Received: 27.06.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:10, 19–36

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