The mixed \(L^{q}\)-spectra of self-conformal measures satisfying the weak separation condition
type: Item
instance of: scholarly article
title: The mixed \(L^{q}\)-spectra of self-conformal measures satisfying the weak separation condition
zbMATH Open document ID: 1228.28009
author: Meifeng Dai
author: Wenwen Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-07-18T00:00:00Z
review text: The mixed \(L^q\)-spectra of measures \(\mu_1,\dots, \mu_k\) is denoted by \(D(q)=\overline D(q)=\underline D(q)\), with the upper \(\overline D(q)= \limsup_{r\to 0}{\log I(r,q)\over -\log r}\) and lower \(\underline D(q)= \liminf_{r\to 0} {\log I(r,q)\over -\log r}\) mixed \(L^q\)-spectra, and \[ I(r,q)= \int \mu_1(B(x_1, r))^{q_1}\cdots \mu_k(B(x_k, r))^{q_k} d\mu(x_1,\dots, x_k). \] Theorem. Let \((\{S_i\}^N_{i=1},\{p_{ji}\}^N_{i=1})\), \(j= 1,\dots, k\), be conformal iterated function system that have the bounded distortion property and satisfy the weak separation condition), then \(\overline D(q)=\underline D(q)\equiv\beta(q)\), \(q= (q_1,\dots, q_k)\in \mathbb{R}^k\).
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5925545
zbMATH Keywords: mixed \(L^q\)-spectra
zbMATH Keywords: self-conformal measure
zbMATH Keywords: bounded distortion property
zbMATH Keywords: weak separation condition
reviewed by: Su Weiyi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.04.037
OpenAlex ID: W2000500103
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DOI: 10.1016/J.JMAA.2011.04.037
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description: scientific article; zbMATH DE number 5925545