Homogeneous Function Spaces

Abstract

A we mentioned in the Preface, Part II of this book deals with further types of function spaces which are more or less closely related to the spaces $B_p^S$,q(R _n ) and $F_p^S$,q(R _n ) from Chapter 2 and their counterparts on domains in Chapter 3. There are many possible modifications and we discuss a few of them. We restrict ourselves to formulations, comments, and occasionally to outlines of some basic ideas. As far as detailed proofs are concerned the reader is asked to consult the quoted references. In many cases the omitted proofs are more or less obvious modifications of corresponding proofs in Chapter 2. We shall give hints. This chapter deals with homogeneous spaces, which are very close to the "non-homogeneous" spaces from the second chapter. The periodic counterparts of these spaces are studied in Chapter 9. Chapters 7 and 8 deal with weighted counterparts. The necessary preparations for these two chapters will be given in Chapter 6. It deals with weighted spaces of entire analytic functions, and is a generalization and modification of the first chapter. Finally, in Chapter 10 we list very briefly further possibilities.