  The fundamental theorem in the theory of the uniform convergence of sine
series is due to Chaundy and Jolliffe from 1916 (see [1]). Several authors gave
conditions for this problem supposing that coefficients are monotone,
non-negative or more recently, general monotone (see [8], [6] and [3], for
example). There are also results for the regular convergence of double sine
series to by uniform in case the coefficients are monotone or general monotone
double sequences. In this article we give new sufficient conditions for the
uniformity of the regular convergence of double sine series, which are
necessary as well in case the coefficients are non-negative. We shall
generalize those results defining a new class of double sequences for the
coefficients.
