L(1)-CONVERGENCE OF DOUBLE FOURIER-SERIES

[摘要] We prove the convergence in L(1)-norm of the double Fourier series of an integrable function f(x, y) which is 2 pi-periodic with respect to x and y, with coefficients a(jk) satisfying certain conditions of the Hardy-Karamata kind, and such that a(jk) log j log k --> 0 as j, k --> infinity. We consider separately double cosine, sine, cosine-sine, and complex trigonometric series. (C) 1994 Academic Press, Inc.

[发布日期] 1994-08-15