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Envelopes and Sharp Embeddings of Function Spaces

Envelopes and Sharp Embeddings of Function Spaces by Dorothee D. Haroske
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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
CRC Press; September 2006
239 pages; ISBN 9781584887515
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Title: Envelopes and Sharp Embeddings of Function Spaces
Author: Dorothee D. Haroske
 
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