Convergence in measure and Weyl multipliers for absolute summability of double function series
Keywords:
double function series, convergence in measure, powers of partial sums, the space l^p, absolute summability, Weyl multipliers, summability factors, Cesaro method, weighted means method
Abstract
In this article a quantitative relation between the partial sums of the double function series ∑m,ncmnfmn(x) and the double sequence (cmn) of its coefficients is established. Estimates of powers of the partial sums of the double function series are given and Weyl multipliers for absolute summability almost everywhere by triangular matrix methods are obtained.
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