On the mixed Bourgain-Morrey spaces

TL;DR

This paper introduces mixed Bourgain-Morrey spaces, explores their properties, duals, and boundedness of key operators, and applies these results to wavelet characterizations and fractional calculus.

Contribution

It defines and studies the properties of mixed Bourgain-Morrey spaces, including duality, boundedness of operators, and applications to wavelets and fractional calculus.

Findings

Boundedness of Hardy-Littlewood maximal operator on these spaces

Establishment of Littlewood-Paley theory for the spaces

Wavelet characterizations and fractional chain rule applications

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. The Littlewood-Paley theory for mixed Bourgain-Morrey spaces and their preduals are established. As applications, we consider wavelet characterizations for mixed Bourgain-Morrey spaces and a fractional chain rule in mixed Bourgain-Morrey Triebel-Lizorkin spaces. In addition, we give a description of the dual of mixed Bourgain-Morrey spaces and conclude the reflexivity of these spaces.