2016; Physical and Mathematical Sciences, 50(1 (239): 22–29
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ON QUASI-UNIVERSAL WALSH SERIESINLp[0,1],p∈[1,2]

Melikbekyan Melikbekyan*

Received: 2025-02-11 · Published: 2016-03-18

© 2016 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON QUASI-UNIVERSAL WALSH SERIESINLp[0,1],p∈[1,2]
Author
Melikbekyan Melikbekyan
Published
2016-03-18
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PSYU:A/2016.50.1.022

Abstract

Let the sequence{ak}∞k=1,ak↘0 with{ak}∞k=1/∈l2,and Walsh system{Wk(x)}∞k=0be given.Then for anyε>0 there exists a measurable setE⊂[0,1]with measure|E|>1−εand numbersδk=±1,0 such that foranyp∈[1,2]and each functionf(x)∈Lp(E)there exists a rearrangementk→σ(k)such that the series∞∑k=1δσ(k)aσ(k)Wσ(k)(x)converges tof(x)in thenorm ofLp(E).
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