Lacunary measures and self-similar probability measures in function spaces
type: Item
instance of: scholarly article
title: Lacunary measures and self-similar probability measures in function spaces
zbMATH Open document ID: 1069.46019
author: Hans Triebel
publication date: 2005-01-25T00:00:00Z
review text: Let \(\mu\) be a Radon measure with bounded support of Lebesgue measure zero. In multifractal geometry, one consideres the quantity \[ \mu^\lambda_{p,q}= \biggl(\sum_j 2^{j\lambda q} \biggl(\sum_m \mu(Q_{j,m})^p\biggr)^{q/p}\biggr)^{1/q}, \] \(\lambda\in {\mathbb R}\) and \(Q_{j,m}\) denotes a standard dyadic cube. Let \(t=\frac 1 p\) and \(\lambda_\mu(\frac 1 p)=\sup\{\lambda:\, \mu^\lambda_{p,q}<\infty\}\). One can consider an analytical characterization of the measure \(\mu\) of the form \(s_\mu(\frac 1 p)=\sup\{s: \mu\in B^s_{p,q}({\mathbb R}^n)\}\). The Radon measure \(\mu\) is called tame if \(s_f(\frac 1 p)= \lambda^f(\frac 1 p)+ n(\frac 1 p - 1)\). The aim of the paper under review is to find sufficient conditions for a Radon measure \(\mu\) to be tame. It is proven that some lacunary measures and special self-similar probability measures are tame.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 2130966
zbMATH Keywords: Besov spaces
zbMATH Keywords: multifractal quantities
zbMATH Keywords: self-similar measures
MaRDI profile type: Publication
full work available at URL: s10114-004-0381-8
OpenAlex ID: W2066221586
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DOI: 10.1007/S10114-004-0381-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2130966