Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces
Bokayev N. Matin D. Akhazhanov T. Adilkhanov A.
January 2024Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2024#12Issue 2
In this paper, we give the sufficient conditions for the compactness of sets in generalized Morrey spaces (Formula presented.). This result is an analogue of the well-known Fréchet–Kolmogorov theorem on the compactness of a set in Lebesgue spaces (Formula presented.) As an application, we prove the compactness of the commutator of the Riesz potential (Formula presented.) in generalized Morrey spaces, where (Formula presented.) ((Formula presented.) denote the (Formula presented.) -closure of (Formula presented.)). We prove auxiliary statements regarding the connection between the norm of average functions and the norm of the difference of functions in the generalized Morrey spaces. Such results are also of independent interest.
commutator , compactness , generalized Morrey space , Riesz potential , VMO
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Department of Fundamental Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov, Eurasian National University, Astana, 010000, Kazakhstan
Higher Mathematics Department, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, 010000, Kazakhstan
Department of Fundamental Mathematics
Higher Mathematics Department
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