Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces

Nurzhan Bokayev, Victor Burenkov, Dauren Matin () and Aidos Adilkhanov
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Nurzhan Bokayev: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Victor Burenkov: V.A. Steklov Mathematical Institute, Russian Academy of Sciences, 42 Gubkin St, 117966 Moscow, Russia
Dauren Matin: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Aidos Adilkhanov: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan

Mathematics, 2024, vol. 12, issue 22, 1-20

Abstract: In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces G M p θ w ( · ) . Our main result is the compactness of the commutators of the Riesz potential b , I α in global Morrey-type spaces from G M p 1 θ 1 w 1 ( · ) to G M p 2 θ 2 w 2 ( · ) . We also present new sufficient conditions for the commutator b , I α to be bounded from G M p 1 θ 1 w 1 ( · ) to G M p 2 θ 2 w 2 ( · ) . In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential b , I α in global Morrey-type spaces G M p θ w ( · ) , and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces G M p θ w ( · ) .

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