ABSTRACT
In this chapter, the authors recall some fundamental inequalities as well as important theorems. The starting point is the review of the theory of Lebesgue spaces. Since Morrey spaces are main function spaces, they take up Morrey spaces. Having defined Morrey spaces and related function spaces, the authors considers local Morrey spaces, which are closely related to Morrey spaces and also consider different function spaces (Banach lattices). They then consider distribution functions of measurable functions to replace Lebesgue spaces with other function spaces, while as another method of replacing Lebesgue spaces they deal with Orlicz spaces, which is different from other sections but still fundamental, introduces Sobolev spaces and Holder–Zygmund spaces, although they are not Banach lattices. The authors recall some fundamental properties on integration theory including Lebesgue spaces. This will be useful when considering Morrey spaces since Lebesgue spaces are realized as a special case of Morrey spaces.
