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

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.

We have divided our article `On the mixed Bourgain-Morrey spaces' (arXiv:2511.08118) into two parts; this is the first part