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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.
Georgian Mathematical Journal – de Gruyter
Published: Aug 1, 2021
Keywords: Generalized weighted (central) Morrey spaces; fractional maximal operator; Riesz potential; weight; 42B25; 42B35; 46E30
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