This article is cited in 1 paper

Short notes

Analogue of the Hardy–Littlewood criterion for Fourier series over Vilenkin system in the case of unbounded $p_k$

S. M. Voronov

D. Mendeleev University of Chemical Technology of Russia

Abstract: Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of analogue of Hardy–Littlewood test and its consequences, which were earlier obtained in the case of bounded sequence $\{p_k\}$ defining the system, are proved.

Key words: zero-dimensional group, characters of a group, Fourier series, Hardy–Littlewood test, Vilenkin system.

UDC: 517.518.43

Received: 15.03.2019

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2020, 75:2, 80–82

Bibliographic databases:

• 
• 
• 
•