Function spaces and distributions

Abstract

This chapter is devoted to function and distribution spaces. We first recall definitions of some well-known classical function and distribution spaces, simultaneously introducing the terminology and notations used in this book. Then we introduce (see Section 1.10) a new class of test functions and the corresponding space of distributions (generalized functions), which play an important role in the theory of pseudo-differential operators with singular symbols introduced in Chapter 2 By singular symbols we mean, if not otherwise assumed, symbols singular in dual variables.