Spaces of smooth functions

E. HARBOURE

Advanced Courses in Mathematical Analysis

WORLD SCI PUBL CO INC

Año: 2008; p. 67 - 85

We will pose several situaions in analysis where some classes of smooth functions play a fundamental role. In connection with the study  of laplace equation, we shall analyze the behavior of the fractional integral operator on Lebesgue spaces, where BMO and Lpschitz spaces arise in a natural way. As a generalization, we will present and study a family of spaces introduced by Spanne. In particular we will be interested in identifying those members in the family containing only continuous functions.