Commutators of Calderón–Zygmund Operators in Grand Variable Exponent Morrey Spaces, and Applications to PDEs

In this note we present the boundedness results for commutators of Calderón–Zygmund operators in grand variable exponent Morrey spaces. The operators and spaces are defined on quasi–metric measure spaces with doubling measure. These results are new even for bounded domains in \({\Bbb {R}}^n\) . The proved statements are applied to study regularity properties of solutions of second order partial differential equations with discontinuous coefficients in the frame of grand variable exponent Morrey spaces.