An extension of Muchenhoupt-Wheeden theorem to generalized weighted (central) Morrey spaces

2018/06/29 by Rza Mustafayev, Mustafayev, Rza, Abdulhamit Kucukaslan +1
Mathematics · #42B25 #42B35 #46E30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:42B25 #msc:42B35 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1806.11367

18 pages

arxiv created 2018/06/29 · arxiv updated 2018/07/02

Abstract

In this paper we find the condition on function ω and weight v which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces \mathcal M_p,ω(\mathbb Rⁿ,v) and generalized weighted central Morrey spaces \mathcal M_p,ω(\mathbb Rⁿ,v), when v belongs to Muckenhoupt A_∞-class.

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• Muckenhoupt-type conditions on weighted Morrey spaces
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• Morrey meets Muckenhoupt: A note on Nakai's generalized Morrey spaces and applications