II Basic Function Spaces and Related Inequalities

Abstract

In this chapter we shall introduce some function spaces and enucleate certain properties of fundamental importance for further developments. Particular emphasis will be given to what are called homogeneous Sobolev spaces, which will play a fundamental role in the study of flow in exterior domains. We shall not attempt, however, to give an exhaustive treatment of the subject, since this is beyond the scope of the book. Therefore, the reader who wants more details is referred to the specialized literature quoted throughout. As a rule, we give proofs where they are elementary or relevant to the development of the subject, or also when the result is new or does not seem to be widely known.