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Eurasian Mathematical Journal, 2012, Volume 3, Number 2, Pages 31–52 (Mi emj85)  
This article is cited in 1 scientific paper (total in 1 paper)

Trigonometric series with lacunary-monotone coefficients

M. I. Dyachenkoa, S. Tikhonovbc

a M. V. Lomonosov Moscow State University, Moscow, Russia
b Centre de Recerca Matemàtica, Barcelona, Spain
c ICREA, Barcelona, Spain
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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.
Received: 13.01.2012
Bibliographic databases:
Document Type: Article
MSC: 42B05, 41A25, 42B35
Language: English
Citation: M. I. Dyachenko, S. Tikhonov, “Trigonometric series with lacunary-monotone coefficients”, Eurasian Math. J., 3:2 (2012), 31–52
Citation in format AMSBIB
\Bibitem{DyaTik12}
\by M.~I.~Dyachenko, S.~Tikhonov
\paper Trigonometric series with lacunary-monotone coefficients
\jour Eurasian Math. J.
\yr 2012
\vol 3
\issue 2
\pages 31--52
\mathnet{http://mi.mathnet.ru/emj85}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3024119}
\zmath{https://zbmath.org/?q=an:1266.42014}
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