2014/07/06 by Episkoposian, S. A.
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1407.1495
In this paper we consider a question on existence of double series by generalized Walsh system, which are 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 ∑n,k=1^∞ | cn,k |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.