Parameter depending almost monotonic functions and their applications to dimensions in metric measures spaces
type: Item
instance of: scholarly article
title: Parameter depending almost monotonic functions and their applications to dimensions in metric measures spaces
zbMATH Open document ID: 1179.26037
DOI: 10.1155/2009/929041
author: Natasha Samko
published in: Journal of Function Spaces and Applications
publication date: 2009-06-23T00:00:00Z
review text: Let \(X\) be a metric space with a positive measure \(\mu \) and \(\Omega \) a bounded open set in \(X\) with \(l=\text{diam\,}\Omega ,0<l<\infty \). The author studies functions \(w(x,r)\) defined on \(\Omega \times \left[ 0,l\right] \) which are almost increasing in the variable \(r,\) thus \(w(x,r_{1})\leq C_{w}w(x,r_{2})\) for \(0\leq r_{1}\leq r_{2}\leq l,\) \(x\in \Omega \), with \(1\leq C_{w}<\infty \). The index numbers \(m(w,x),M(w,x)\) of such functions and some generalized Zygmund, Bary, Lozinskii and Stechkin conditions are considered. Conditions for the uniform belonging of functions \(w(.,r)\) to Zygmund-Bary-Stechkin classes are determined.
reviewed by: Gheorghe Toader
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 5568059
zbMATH Keywords: Zygmund conditions
zbMATH Keywords: Zygmund-Bary-Stechkin class
zbMATH Keywords: measure metric space
zbMATH Keywords: indices of monotonic functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/929041
OpenAlex ID: W2107780580
description: scientific article; zbMATH DE number 5568059