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An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces

An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces AbstractIn this paper, we find the condition on a function ω and a weight v which ensuresthe equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces ℳp,ω⁢(ℝn,v){{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)} and generalized weighted central Morrey spaces ℳ˙p,ω⁢(ℝn,v){\dot{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)}, when v belongs to the Muckenhoupt A∞{A_{\infty}}-class. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces

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References (40)

Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2020-2056
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we find the condition on a function ω and a weight v which ensuresthe equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces ℳp,ω⁢(ℝn,v){{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)} and generalized weighted central Morrey spaces ℳ˙p,ω⁢(ℝn,v){\dot{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)}, when v belongs to the Muckenhoupt A∞{A_{\infty}}-class.

Journal

Georgian Mathematical Journalde Gruyter

Published: Aug 1, 2021

Keywords: Generalized weighted (central) Morrey spaces; fractional maximal operator; Riesz potential; weight; 42B25; 42B35; 46E30

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