Existence of double Walsh series universal in weighted L_μ¹[0,1]² spaces

2015/01/05 by Sergo A. Episkoposian, Episkoposian, Sergo A.
Mathematics · #42C10 #42C20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1501.00829

openalex publication_date 2015/01/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a question on existence of double Walsh series universal in weighted L_μ¹[0,1]² spaces. We construct a weighted function μ(x,y) and a series by double Walsh system of the form ∑_n,k=1^∞ c_n,kW_n(x)W_k(y) with ∑_n,k=1^∞ | c_n,k |^q 2, which is universal in L_μ¹[0,1]² concerning subseries with respect to convergence, in the sense of both spherical and rectangular partial sums.

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