Littlewood-Paley and wavelet characterization for mixed Morrey spaces

In this paper, we consider the Littlewood-Paley characterization for mixed Morrey spaces and its predual spaces. The topology to converge the Littlewood-Paley decomposition for the element of mixed Morrey spaces is the weak-* topology. If we consider the topology of mixed Morrey spaces, we must give other characterization by using the heat semigroup. As an application, we show the wavelet characterization for mixed Morrey spaces. In particular, this characterization can be shown without the Peetre maximal operator.