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

Abstract

In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces GMw(·) pθ . Our main result is the compactness of the commutators of the Riesz potential [b, Iα] in global Morrey-type spaces from GMw1(·) p1θ1 to GMw2(·) p2θ2 . We also present new sufficient conditions for the commutator [b, Iα] to be bounded from GMw1(·) p1θ1 to GMw2(·) p2θ2 . 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 GMw(·) pθ , and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces GMw(·) pθ .