zbMATH — the first resource for mathematics

On the maximum of the rectangular partial sums of double trigonometric series with nonnegative coefficients. (English) Zbl 0756.42010
The author proves a necessary and sufficient condition for integrability of the maximum of the partial sums of the double cosine and sine series with monotone coefficients as well as a sufficient one for pointwise and normwise convergence of these series. The results are two-dimensional analogues of a result of S. B. Stechkin [Usp. Mat. Nauk 18, No. 1(109), 173–180 (1963; Zbl 0113.27502)], but which have been obtained in a different way.
42B05 Fourier series and coefficients in several variables