Abstract
Let be multilinear fractional integral operator and let . In this paper, the estimates of , the m-linear commutators and the iterated commutators on the generalized weighted Morrey spaces are established. MSC:42B35, 42B20.
Highlights
Introduction and resultsThe classical Morrey spaces were introduced by Morrey [ ] in, have been studied intensively by various authors, and together with weighted Lebesgue spaces play an important role in the theory of partial differential equations; they appeared to be quite useful in the study of local behavior of the solutions of elliptic differential equations and describe local regularity more precisely than Lebesgue spaces
Various Morrey spaces have been defined in the process of this study
Mizuhara [ ] introduced the generalized Morrey space Mφp ; Komori and Shirai [ ] defined the weighted Morrey spaces Lp,κ (ω); Guliyev [ ] gave the concept of generalized weighted Morrey space Mφp(ω), which could be viewed as an extension of both Mφp and Lp,κ (ω)
Summary
Introduction and resultsThe classical Morrey spaces were introduced by Morrey [ ] in , have been studied intensively by various authors, and together with weighted Lebesgue spaces play an important role in the theory of partial differential equations; they appeared to be quite useful in the study of local behavior of the solutions of elliptic differential equations and describe local regularity more precisely than Lebesgue spaces. More results of the weighted inequalities for multilinear fractional integral and its commutators can be found in [ – ]. The aim of the present paper is to investigate the boundedness of multilinear fractional integral operator and its commutator on the generalized weighted Morrey spaces.
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