On the existence and structure of universal functions for weighted spaces [Formula omitted]

On the existence and structure of universal functions for weighted spaces [Formula omitted]

In the paper it is shown that there exist a set [Formula omitted] with the measure being arbitrarily close to 1 and a weighted function [Formula omitted] with [Formula omitted] on E, so that with a proper modification of an arbitrary function [Formula omitted] outside E one can obtain a function [Fo...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) Vol. 271; no. 5; pp. 644 - 657
Main Authors: Grigoryan, M. G, Sargsyan, A.A
Format: Journal Article
Language:English
Published: Springer 01-04-2023
Online Access:Get full text
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Summary:In the paper it is shown that there exist a set [Formula omitted] with the measure being arbitrarily close to 1 and a weighted function [Formula omitted] with [Formula omitted] on E, so that with a proper modification of an arbitrary function [Formula omitted] outside E one can obtain a function [Formula omitted] being universal for the weighted space [Formula omitted] with respect to Walsh system in the sense of signs.
ISSN:1072-3374
DOI:10.1007/s10958-023-06439-5