M. I. Dyachenko, E. D. Nursultanov, “Hardy-Littlewood theorem for trigonometric series with <nobr>$\alpha$</nobr>-monotone coefficients”, Mat. Sb., 2009, Volume 200, Number 11,Pages <nobr>45

This article is cited in 7 papers

Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients

M. I. Dyachenko^a, E. D. Nursultanov^bc

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Kazakhstan Branch of Lomonosov Moscow State University
^c L. N. Gumilev Eurasian National University

Abstract: The Hardy-Littlewood theorem is established for trigonometric series with $\alpha$-monotone coefficients. Inequalities of Hardy-Littlewood kind are proved. Examples of series demonstrating that the results obtained are sharp are constructed.
Bibliography: 15 titles.

Keywords: generalized monotone coefficients, Hardy-Littlewood theorem.

UDC: 517.52

MSC: 42A16

Received: 03.12.2008 and 13.04.2009

DOI: 10.4213/sm7510