Аннотации:
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
.
