ABSTRACT
This chapter introduces the main function spaces and collects some of their remarkable properties that will be extensively used. It considers spaces of (Holder) continuous functions and proves some very important interpolation estimates. The chapter introduces anisotropic and parabolic spaces of Holder continuous functions, which appear naturally in the analysis of optimal regularity for classical solutions to parabolic equations. It describes the Besov spaces which are intrinsically related to the theory of traces of functions which belongs to Sobolev spaces over (sufficiently smooth) domains. The chapter explains the main results of the classical theory and Sobolev spaces. It also explains some propositions, and proves very useful interpolation results.
