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

Nurzhan Bokayev, Victor I. Burenkov, Dauren Matin, A.N. Adilkhanov

Mathematics, 2024

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DOI 10.3390/math12223533
Data confidence 70 medium
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Abstract

In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces GMpθw(·). Our main result is the compactness of the commutators of the Riesz potential b,Iα in global Morrey-type spaces from GMp1θ1w1(·) to GMp2θ2w2(·). We also present new sufficient conditions for the commutator b,Iα to be bounded from GMp1θ1w1(·) to GMp2θ2w2(·). 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,Iα in global Morrey-type spaces GMpθw(·), and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces GMpθw(·).