M. I. Dyachenko, S. Tikhonov, “Trigonometric series with lacunary-monotone coefficients”, Eurasian Math. J., 2012, Volume 3, Number 2,Pages <nobr>31

This article is cited in 1 paper

Trigonometric series with lacunary-monotone coefficients

M. I. Dyachenko^a, S. Tikhonov^bc

^a M. V. Lomonosov Moscow State University, Moscow, Russia
^b Centre de Recerca Matemàtica, Barcelona, Spain
^c ICREA, Barcelona, Spain

Abstract: In this paper we study multiple trigonometric series with lacunary-monotone coefficients. We obtain necessary and sufficient conditions for the sum of such series to belong to $L_p$, $1<p\le\infty$ and the generalized Lipschitz spaces (Nikol'skii spaces).

Keywords and phrases: multiple trigonometric series, lacunary-monotone coefficients, Lipschitz and Nikol’skii spaces.

MSC: 42B05, 41A25, 42B35

Received: 13.01.2012

Language: English