This article is cited in 1 paper

Sets of absolute convergence of double trigonometric series

R. A. Avetisyan

M. V. Lomonosov Moscow State University

Abstract: We obtain a sufficient condition for a set of plane measure zero to be a set of absolute convergence (an A.C.-set) for a double trigonometric series. Specifically, let $y=f(x)$ ($0\leqslant x\leqslant2\pi$) be a smooth curve and let $\bigvee\limits_0^{2\pi}\ln|f'(x)|<\infty$. Then, any set of positive linear measure lying on this curve is an A.C.-set.

UDC: 517.5

Received: 25.06.1971

 English version: Mathematical Notes, 1972, 11:5, 289–293

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