Properties of a generalized class of weights satisfying reverse Hölder's inequality
type: Item
instance of: scholarly article
title: Properties of a generalized class of weights satisfying reverse Hölder's inequality
zbMATH Open document ID: 1462.42033
DOI: 10.1155/2021/5515042
author: Yanyan Li
published in: Journal of Function Spaces
publication date: 2021-05-03T00:00:00Z
review text: Summary: In this paper, we will prove some fundamental properties of the discrete power mean operator \(\mathcal{M}_p u(n)= (1/n\sum_{k=1}^n u^p (k))^{1 / p}\), for \(n\in\mathbb{I}\subseteq \mathbb{Z}_+,\) of order \(p\), where \(u\) is a nonnegative discrete weight defined on \(\mathbb{I}\subseteq \mathbb{Z}_+\) the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of different operators with different powers. Next, we will study the structure of the generalized discrete class \(\mathcal{B}_p^q(B)\) of weights that satisfy the reverse Hölder inequality \(\mathcal{M}_q u\leq B\mathcal{M}_pu\), for positive real numbers \(p\), \(q\), and \(B\) such that \(0<p<q\) and \(B>1\). For applications, we will prove some self-improving properties of weights from \(\mathcal{B}_p^q(B)\) and derive the self improving properties of the discrete Gehring weights as a special case. The paper ends by a conjecture with an illustrative sharp example.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42A24
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 7341747
zbMATH Keywords: discrete power mean operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5515042
OpenAlex ID: W3129201156
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description: scientific article; zbMATH DE number 7341747