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July 2019 On the structure of universal functions for classes Lp[0,1)2,p(0,1), with respect to the double Walsh system
Martin Grigoryan, Artsrun Sargsyan
Banach J. Math. Anal. 13(3): 647-674 (July 2019). DOI: 10.1215/17358787-2019-0015

Abstract

We address questions on the existence and structure of universal functions for classes Lp[0,1)2, p(0,1), with respect to the double Walsh system. It is shown that there exists a measurable set E[0,1)2 with measure arbitrarily close to 1, such that, by a proper modification of any integrable function fL1[0,1)2 outside E, we can get an integrable function f˜L1[0,1)2, which is universal for each class Lp[0,1)2, p(0,1), with respect to the double Walsh system in the sense of signs of Fourier coefficients.

Citation

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Martin Grigoryan. Artsrun Sargsyan. "On the structure of universal functions for classes Lp[0,1)2,p(0,1), with respect to the double Walsh system." Banach J. Math. Anal. 13 (3) 647 - 674, July 2019. https://doi.org/10.1215/17358787-2019-0015

Information

Received: 10 November 2018; Accepted: 2 March 2019; Published: July 2019
First available in Project Euclid: 20 June 2019

zbMATH: 07083766
MathSciNet: MR3978942
Digital Object Identifier: 10.1215/17358787-2019-0015

Subjects:
Primary: 42C10
Secondary: 43A15

Keywords: convergence in metric , Fourier coefficients , universal function , Walsh system

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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