Universality Properties of a Double Series by the Generalized Walsh System

Abstract EN

We consider a question on existence of a double series by the generalized Walsh system, which is universal in weighted Lμ1[0,1]2 spaces.

In particular, we construct a weighted function μ(x,y) and a double series by generalized Walsh system of the form ∑n,k=1∞cn,kψn(x)ψk(y) with the ∑n,k=1∞|cn,k|q<∞ for all q>2, which is universal in Lμ1[0,1]2 concerning subseries with respect to convergence, in the sense of both spherical and rectangular partial sums.