## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 11, Number 3 (2017), 698-712.

### On the universal and strong $({L}^{1},{L}^{\infty})$-property related to Fourier–Walsh series

#### Abstract

In this article, we construct a function $U\in {L}^{1}[0,1)$ with strictly decreasing Fourier–Walsh coefficients $\left\{{c}_{k}\right(U\left)\right\}\searrow $, and having a universal and strong $({L}^{1},{L}^{\infty})$-property with respect to the Walsh system.

#### Article information

**Source**

Banach J. Math. Anal., Volume 11, Number 3 (2017), 698-712.

**Dates**

Received: 25 July 2016

Accepted: 12 October 2016

First available in Project Euclid: 16 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1494900292

**Digital Object Identifier**

doi:10.1215/17358787-2017-0012

**Mathematical Reviews number (MathSciNet)**

MR3679902

**Zentralblatt MATH identifier**

1376.42037

**Subjects**

Primary: 42A65: Completeness of sets of functions

Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series

**Keywords**

universal function Fourier–Walsh coefficients

#### Citation

Grigoryan, Martin G. On the universal and strong $(L^{1},L^{\infty})$ -property related to Fourier–Walsh series. Banach J. Math. Anal. 11 (2017), no. 3, 698--712. doi:10.1215/17358787-2017-0012. https://projecteuclid.org/euclid.bjma/1494900292