Convergence of sequences of two-dimensional Fejer means of trigonometric Fourier series of integrable functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Gat, Gyoergy

关键词: Trigonometric system;    Two-dimensional Fejer means;    Subsequence;    Almost everywhere convergence;   

DOI  :  10.1016/j.jmaa.2012.01.038

来源: Elsevier

【 摘 要 】

The aim of this paper is to prove the a.e. convergence of sequences of the Fejer means of the trigonometric Fourier series of two variable integrable functions. That is, let a = (a(1), a(2)): N -> N-2 such that a(j)(n+1) >= alpha SUPk <= n a(j)(k) (j=1,2, n is an element of N) for some alpha >0 and a(1) (+infinity) = a(2) (+infinity) = +infinity. Then for each integrable function f is an element of L-1 (T-2) we have the ac. relation lim(n ->infinity)sigma(a(n)) f = f. It will be a straightforward and easy consequence of this result the historical cone restricted se. convergence result with respect to the two-dimensional Fejer means of integrable functions due to Marcinkiewicz and Zygmund (1939) [7]. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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