Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces

Nurzhan Bokayev, Dauren Matin (), Talgat Akhazhanov and Aidos Adilkhanov
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Nurzhan Bokayev: Department of Fundamental Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Dauren Matin: Higher Mathematics Department, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Talgat Akhazhanov: Higher Mathematics Department, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Aidos Adilkhanov: Department of Fundamental Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan

Mathematics, 2024, vol. 12, issue 2, 1-16

Abstract: In this paper, we give the sufficient conditions for the compactness of sets in generalized Morrey spaces M p w ( · ) . This result is an analogue of the well-known Fréchet–Kolmogorov theorem on the compactness of a set in Lebesgue spaces L p , p > 0 . As an application, we prove the compactness of the commutator of the Riesz potential [ b , I α ] in generalized Morrey spaces, where b ∈ V M O ( V M O ( R n ) denote the B M O -closure of C 0 ∞ ( R n ) ). 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.

Keywords: commutator; Riesz potential; compactness; generalized Morrey space; VMO (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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