The local trace inequality for potential type integral operators
type: Item
instance of: scholarly article
title: The local trace inequality for potential type integral operators
zbMATH Open document ID: 1266.42049
author: Hitoshi Tanaka
author: Hendra Gunawan
published in: Potential Analysis
publication date: 2013-02-15T00:00:00Z
review text: The local trace inequality for the following operators of potential type \(T_{\rho}\) is obtained in the context of Morrey spaces: Let \({\mathcal D}\) be the set of all dyadic cubes \(Q \in \mathbb{R^N}\) which intersect the support of the locally finite nonnegative Borel measure \(\sigma\) on \(\mathbb{R^N}\) and let \(\rho:{\mathcal D}\longrightarrow \mathbb{R}^+\) be a map. For a locally \(\sigma-\)integrable function \(f\) on \(\mathbb{R}^N\), the potential type \(T_{\rho}\) is defined by \[ T_{\rho}f(x)=\sum_{Q\in {\mathcal D}} \frac{\rho(Q)}{\sigma(Q)} \int_{3Q} f(y) \;d\sigma(y) \chi_Q(x) \quad x\in \mathbb{R^N}. \] Some applications of the main results are obtained such as an improvement of the Olsen inequality in this context. Also a sufficient condition is obtained for the equivalence between the Kerman-Sawyer condition and the Adams condition that are involved to obtain the local trace inequality.
reviewed by: Santiago Boza
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 6136724
zbMATH Keywords: Morrey space
zbMATH Keywords: potential type integral operator
zbMATH Keywords: trace inequality
zbMATH Keywords: Olsen inequality
MaRDI profile type: Publication
full work available at URL: s11118-012-9291-z
OpenAlex ID: W1980573265
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DOI: 10.1007/S11118-012-9291-Z
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description: scientific article; zbMATH DE number 6136724