Abstract
In this Note we study the convergence results for trigonometric series in L p -spaces on one-dimensional and n-dimension torus. The sufficient conditions for these results to hold as well as criteria are written for the series with general monotone coefficients. The Hardy–Littlewood type theorem is obtained for multiple series. Several corollaries, in particular, u-convergence are presented. To cite this article: M. Dyachenko, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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