Banach Journal of Mathematical Analysis

On the structure of universal functions for classes Lp[0,1)2,p(0,1), with respect to the double Walsh system

Martin Grigoryan and Artsrun Sargsyan

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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.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 647-674.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1560996143

Digital Object Identifier
doi:10.1215/17358787-2019-0015

Mathematical Reviews number (MathSciNet)
MR3978942

Zentralblatt MATH identifier
07083766

Subjects
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

Keywords
universal function Fourier coefficients Walsh system convergence in metric

Citation

Grigoryan, Martin; Sargsyan, Artsrun. On the structure of universal functions for classes $L^{p}[0,1)^{2},p\in (0,1)$ , with respect to the double Walsh system. Banach J. Math. Anal. 13 (2019), no. 3, 647--674. doi:10.1215/17358787-2019-0015. https://projecteuclid.org/euclid.bjma/1560996143


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