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.
