An inverse Sidon type inequality for the Walsh system
type: Item
instance of: scholarly article
title: An inverse Sidon type inequality for the Walsh system
zbMATH Open document ID: 0836.42017
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-04-23T00:00:00Z
review text: Sidon inequalities, upper estimates of integral norms of Dirichlet kernels, have a long and interesting history whose latest chapter began with the paper by \textit{R. Bojanić} and \textit{C. V. Stanojević} [Trans. Am. Math. Soc. 269, 677-683 (1982; Zbl 0493.42011)]. Although each paper tended to offer some small improvement over one of its predecessors, no one had given serious consideration to where all this would end. In this paper, the author addresses this question head on by obtaining both upper and lower estimates. The result is the best rearrangement invariant expression of coefficients for a Sidon type inequality. (The expression itself, which bristles with technicalities involving \(\log^+\) of ratios of partial sums, can be associated with an Orlicz norm.) In addition to presenting interesting results, the paper also contains many remarks which bring out the history as well as the applications of Sidon inequalities. It is both well written and informative.
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 811200
zbMATH Keywords: Walsh series
zbMATH Keywords: Sidon inequalities
author: Sándor Fridli
reviewed by: William R. Wade
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1263
OpenAlex ID: W2091878104
DOI: 10.1006/JMAA.1995.1263
description: scientific article; zbMATH DE number 811200