Some embeddings into the Morrey and modified Morrey spaces associated with the Dunkl operator
type: Item
instance of: scholarly article
title: Some embeddings into the Morrey and modified Morrey spaces associated with the Dunkl operator
zbMATH Open document ID: 1198.46027
DOI: 10.1155/2010/291345
author: Emin V. Guliyev
author: Yagub Y. Mammadov
published in: Abstract and Applied Analysis
publication date: 2010-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/233188
review text: Summary: We consider the generalized shift operator associated with the Dunkl operator \(\Lambda_\alpha(f)(x)=(d/dx)f(x)+((2\alpha+1)/x)((f(x)-f(-x))/2)\), \(\alpha>-1/2\). We study some embeddings into the Morrey space (\(D\)-Morrey space) \(L_{p,\lambda,\alpha}\), \(0\leq\lambda<2\alpha +2\), and modified Morrey space (modified \(D\)-Morrey space) \(\widetilde L_{p,\lambda,\alpha}\) associated with the Dunkl operator on \(\mathbb R\). As applications, we get boundedness of the fractional maximal operator \(M_\beta\), \(0\leq\beta<2\alpha+2\), associated with the Dunkl operator (fractional \(D\)-maximal operator) from the spaces \(L_{p,\lambda,\alpha}\) to \(L_\infty(\mathbb R)\) for \(p=(2\alpha+2-\lambda)/\beta\) and from the spaces \(\widetilde L_{p,\lambda,\alpha}(\mathbb R)\) to \(L_\infty(\mathbb R)\) for \((2\alpha+2-\lambda)/\beta\leq p\leq (2\alpha+2)/\beta\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5690922
MaRDI profile type: Publication
OpenAlex ID: W2117182617
Wikidata QID: Q58649813
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description: scientific article; zbMATH DE number 5690922