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

Georgian Mathematical Journal, vol.28, no.4, pp.595-610, 2021 (Journal Indexed in SCI Expanded)

• Publication Type: Article / Article
• Volume: 28 Issue: 4
• Publication Date: 2021
• Doi Number: 10.1515/gmj-2020-2056
• Title of Journal : Georgian Mathematical Journal
• Page Numbers: pp.595-610
• Keywords: fractional maximal operator, Generalized weighted (central) Morrey spaces, Riesz potential, weight

#### Abstract

© 2020 Walter de Gruyter GmbH, Berlin/Boston 2021.In this paper, we find the condition on a function ω and a weight v which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces p,ω(n,v){{\mathcal{M}}-{p,\omega}({\mathbb{R}}^{n},v)} and generalized weighted central Morrey spaces ˙p,ω(n,v){{\mathcal{M}}-{p,\omega}({\mathbb{R}}^{n},v)}, when v belongs to the Muckenhoupt A∞{A-{\infty}}-class.