Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent

2018/12/18 by Vagif S. Guliyev, Guliyev, Vagif S., Javanshir J. Hasanov +3
Mathematics · #42B20 #42B25 #42B35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:42B20 #msc:42B25 #msc:42B35

paper · pdf · doi:10.48550/arxiv.1812.07314

23 pages

arxiv created 2018/12/18 · openalex publication_date 2018/12/18 · arxiv updated 2018/12/19 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝⁿ be an unbounded open set. We consider the generalized weighted Morrey spaces M^p(⋅),φ_ω(Ω) and the vanishing generalized weighted Morrey spaces VM^p(⋅),φ_ω(Ω) with variable exponent p(x) and a general function φ(x,r) defining the Morrey-type norm. The main result of this paper are the boundedness of Riesz potential and its commutators on the spaces M^p(⋅),φ_ω(Ω) and VM^p(⋅),φ_ω(Ω). This result generalizes several existing results for Riesz potential and its commutators on Morrey type spaces. Especially, it gives a unified result for generalized Morrey spaces and variable Morrey spaces which currently gained a lot of attentions from researchers in theory of function spaces.

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