Norm inequalities in generalized Morrey spaces

TL;DR

This paper establishes the boundedness of various classical and singular integral operators, including Calderón-Zygmund and Marcinkiewicz operators, on generalized Morrey spaces, extending their applicability beyond weighted Morrey spaces.

Contribution

It introduces new boundedness results for a broad class of operators on generalized Morrey spaces, expanding the functional analytic framework for these operators.

Findings

Boundedness of Calderón-Zygmund operators on generalized Morrey spaces

Boundedness of Marcinkiewicz and maximal operators in this setting

Extension of operator boundedness to spaces with rough kernels and commutators

Abstract

We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.