ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book considers local Morrey spaces, which are closely related to Morrey spaces and distribution functions of measurable functions. It recalls some fundamental properties on integration theory including Lebesgue spaces. The notion of Banach lattices is used to cover many function spaces. One of the other useful tools to classify function spaces is the use of Banach function spaces. The Hardy operator will play the role of a toy model of the Hardy–Littlewood maximal operator. Hardy’s inequality is a useful inequality that can be used to control some integrals. One of the fundamental techniques in the theory of function spaces is considering function spaces slightly different from Lebesgue spaces. This technique is used especially to compensate for the failure of the boundedness of operators.
