On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces

2013/10/24 by Vagif S. Guliyev, Guliyev, Vagif S., Fatih Deringoz +1 · 2 citations
Mathematics · #42B20 #42B25 #42B35 #46E30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:42B20 #msc:42B25 #msc:42B35 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1310.6604

23 pages. J. Funct. Spaces Appl.(to appear)

arxiv created 2013/12/30 · arxiv updated 2013/12/31

Abstract

We consider generalized Orlicz-Morrey spaces M_Φ,φ(\Rn) including their weak versions WM_Φ,φ(\Rn). In these spaces we prove the boundedness of the Riesz potential from M_Φ,φ1(\Rn) to M_Ψ,φ2(\Rn) and from M_Φ,φ1(\Rn) to WM_Ψ,φ2(\Rn). As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on (φ₁,φ₂), which do not assume any assumption on monotonicity of φ₁(x,r), φ₂(x,r) in r.

Cited by

• Boundedness of Intrinsic Square Functions and their Commutators on Generalized Orlicz-Morrey Spaces
• Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces

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