## Banach Journal of Mathematical Analysis

### On the structure of universal functions for classes $L^{p}[0,1)^{2},p\in (0,1)$, with respect to the double Walsh system

#### Abstract

We address questions on the existence and structure of universal functions for classes $L^{p}[0,1)^{2}$, $p\in (0,1)$, with respect to the double Walsh system. It is shown that there exists a measurable set $E\subset [0,1)^{2}$ with measure arbitrarily close to $1$, such that, by a proper modification of any integrable function $f\in L^{1}[0,1)^{2}$ outside $E$, we can get an integrable function $\tilde{f}\in L^{1}[0,1)^{2}$, which is universal for each class $L^{p}[0,1)^{2}$, $p\in (0,1)$, 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
Accepted: 2 March 2019
First available in Project Euclid: 20 June 2019

https://projecteuclid.org/euclid.bjma/1560996143

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

Mathematical Reviews number (MathSciNet)
MR3978942

Zentralblatt MATH identifier
07083766

#### 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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