On uniform convergence of one class of double trigonometric series

Abstract

We have established sufficient conditions of uniform convergence of the series of the form $\sum\limits_{k,l=1} a_{k,l} \sin kx \sin ly$ in the strip: $-\infty < x < +\infty$, $\delta \leqslant y \leqslant 2\pi - \delta$ ($\delta$ is a fixed number, $0 < \delta < \pi$).