Mixed Bourgain-Morrey spaces and their applications to boundedness of operators

TL;DR

This paper introduces mixed Bourgain-Morrey spaces, explores their duals and reflexivity, and proves the boundedness of key operators like maximal and integral operators on these spaces.

Contribution

It presents the first study of mixed Bourgain-Morrey spaces, including their duals, reflexivity, and operator boundedness properties.

Findings

Boundedness of Hardy-Littlewood maximal operator established

Dual space characterized and reflexivity proven

Boundedness of fractional and singular integral operators demonstrated

Abstract

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved. In addition, we give a description of the dual of mixed Bourgain-Morrey spaces and conclude the reflexivity of these spaces.