Precompact Sets, Boundedness, and Compactness of Commutators for Singular Integrals in Variable Morrey Spaces

Abstract

We give sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Then we obtain the boundedness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Finally, we discuss the compactness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces.

Relatively Compact Sets in Variable Exponent Morrey Spaces on Metric Spaces

“…Theorem 4.2 is new in the constant exponent case, but this question has also been considered in [5]. In [35], some sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Note that in variable exponent Lebesgue spaces (that is for λ(•) := 0), Theorem 4.2 was proved in [3].…”