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arXiv · 1407.1495

Universality properties of double series by generalized Walsh system

S. A. Episkoposian
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Abstract

In this paper we consider a question on existence of double series by generalized Walsh system, which are universal in weighted $L_μ^1[0,1]^2$ spaces. In particular, we construct a weighted function $μ(x,y)$ and a double series by generalized Walsh system of the form $$\sum_{n,k=1}^\infty c_{n,k}ψ_n(x)ψ_k(y)\ \ \mbox{with} \ \ \sum_{n,k=1}^\infty \left | c_{n,k} \right|^q <\infty\ \mbox{for all}\ q>2,$$ which is universal in $L_μ^1[0,1]^2$ concerning subseries with respect to convergence, in the sense of both spherical and rectangular partial sums.

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S. A. Episkoposian. 2014-07-06. Universality properties of double series by generalized Walsh system. https://arxiv.org/abs/1407.1495

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