ABSTRACT
The dual of Morrey spaces contains an element which cannot be expressed in terms of locally integrable functions. However, the Morrey spaces are realized as the dual of Banach function spaces. This chapter introduces the predual of Morrey spaces. It investigates the predual of Morrey spaces, which has some equivalent characterizations. It starts with defining the block spaces and also introduces predual spaces. The chapter considers subspaces in predual spaces and deals with duality. The Fatou property of the function spaces is one of the important properties. As it turns out, among others it is difficult to check the Fatou property of predual spaces. One of the fundamental techniques in the theory of function spaces is to decompose functions into some elementary pieces. As witnessed in the Calderón–Zygmund decomposition, this is useful when analyzing linear operators.
