Envelopes and Sharp Embeddings of Function Spaces

ISBN: 9781584887508 出版年：2006 页码：239 Haroske, Dorothee D CRC Press

Preface DEFINITION, BASIC PROPERTIES, AND FIRST EXAMPLES Introduction Preliminaries, Classical Function Spaces Non-increasing rearrangements Lebesgue and Lorentz spaces Spaces of continuous functions Sobolev spaces Sobolev's embedding theorem The Growth Envelope Function EG Definition and basic properties Examples: Lorentz spaces Connection with the fundamental function Further examples: Sobolev spaces, weighted Lp-spaces Growth Envelopes EG Definition Examples: Lorentz spaces, Sobolev spaces The Continuity Envelope Function EC Definition and basic properties Some lift property Examples: Lipschitz spaces, Sobolev spaces Continuity Envelopes EC Definition Examples: Lipschitz spaces, Sobolev spaces RESULTS IN FUNCTION SPACES AND APPLICATIONS Function Spaces and Embeddings Spaces of type Bsp,q, Fsp,q Embeddings Growth Envelopes EG Growth envelopes in the sub-critical case Growth envelopes in sub-critical borderline cases Growth envelopes in the critical case Continuity Envelopes EC Continuity envelopes in the super-critical case Continuity envelopes in the super-critical borderline case Continuity envelopes in the critical case Envelope Functions EG and EC Revisited Spaces on R+ Enveloping functions Global versus local assertions Applications Hardy inequalities and limiting embeddings Envelopes and lifts Compact embeddings References Symbols Index List of Figures