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On estimating integral moduli of continuity of functions of several variables in terms of Fourier coefficients. (English) Zbl 0949.42009

Double cosine and sine series are considered which converge in Pringsheim’s sense, except possibly when \(x= 0\) or \(y=0\pmod{2\pi}\). The integral moduli of continuity of their sums are estimated in terms of the coefficients of the series in question. The inequalities obtained in this paper extend those by S. A. Telyakovskij [Mat. Sb., N. Ser. 91(133), 537-553 (1973; Zbl 0279.42005)] from single to double trigonometric Fourier series. They are too long to be presented here.

MSC:

42B05 Fourier series and coefficients in several variables

Citations:

Zbl 0279.42005
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