Inclusion of mixed Morrey spaces

The main purpose of this paper is to give some necessary and sufficient conditions for inclusions between mixed Morrey spaces, between iterated weak Morrey spaces, and between a mixed Morrey space and an iterated weak Morrey space. Our proof uses the calculation of the mixed Morrey norm of characteristic functions of balls. Our results extend the inclusion results in Morrey spaces to mixed Morrey spaces and iterated weak Morrey spaces.