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Envelopes and Sharp Embeddings of Function Spaces

Dorothee D. Haroske
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2007
Number of Pages: 
227
Format: 
Hardcover
Series: 
Research Notes in Mathematics Series 437
Price: 
89.95
ISBN: 
1584887508
Category: 
Monograph
We do not plan to review this book.

 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

Dummy View - NOT TO BE DELETED