On The Continuity Of Some Integral Operators On Function Spaces

Abstract

This thesis aims to study the continuity criteria for the Hardy type operators on the variable exponent function spaces. More specifically, in this thesis, we consider the boundedness of the fractional Hardy and rough fractional Hardy operators on Morrey and Herz-type spaces with variable exponents. Similar results for the commutators generated by these operators and variable λ-central bounded mean oscillation (BMO) functions are likewise obtained. Also, the continuity of Hardy-type operators and their commutators on variable exponent function spaces of weighted type took less attention by the research community worldwide. The same is with weighted Morrey and Herz-type space with variable exponents. The present thesis also aims to fill this gap by proving the boundedness of the fractional Hardy type operators, along with their commutators with weighted variable λ-central bounded BMO functions, on these spaces.