Boundedness of Commutators of Singular and Potential Operators in Generalized Grand Morrey Spaces and some applications

TL;DR

This paper proves the boundedness of certain commutators of singular and potential operators in generalized grand Morrey spaces and applies these results to elliptic equation solutions.

Contribution

It introduces boundedness results for commutators in generalized grand Morrey spaces and explores their applications to elliptic PDEs.

Findings

Boundedness of Calderón-Zygmund commutators in generalized grand Morrey spaces

Boundedness of potential operator commutators with BMO functions

Interior estimates for elliptic equations in these spaces

Abstract

In the setting of homogeneous spaces (X,d,{\mu}), it is shown that the commutator of Calder\'on- Zygmund type operators as well as commutator of potential operator with BMO function are bounded in generalized Grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.