Variable Lebesgue spaces : foundations and harmonic analysis
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest sin...
Gardado en:
| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Basel :
Springer Basel
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2013. |
| Series: | Applied and Numerical Harmonic Analysis
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 315 p. Collection de l'édition imprimée : "Applied and Numerical Harmonic Analysis" Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Variable Lebesgue spaces, foundations and harmonic analysis, David V. Cruz-Uribe, Alberto Fiorenza, Heidelberg, Birkhäuser/Springer, 2013, 1 vol. (IX - 312 p.), Applied and numerical harmonic analysis, 978-3-0348-0547-6 • Variable Lebesgue Spaces, Texte imprimé, 9783034805490 • Variable Lebesgue Spaces, Texte imprimé, 9783034807579 |
Table des matières:
- 1 Introduction 2 Structure of Variable Lebesgue Spaces 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity 5 Extrapolation in the Variable Lebesgue Spaces 6 Basic Properties of Variable Sobolev Spaces Appendix: Open Problems Bibliography Symbol Index Author Index Subject Index.
- 1 Introduction
- 2 Structure of Variable Lebesgue Spaces
- 3 The Hardy-Littlewood Maximal Operator
- 4 Beyond Log-Hölder Continuity
- 5 Extrapolation in the Variable Lebesgue Spaces
- 6 Basic Properties of Variable Sobolev Spaces
- 1.1 An Overview of Variable Lebesgue Spaces
- 1.2 A Brief History of Variable Lebesgue Spaces
- 1.3 The Organization of this Book
- 1.4 Prerequisites and Notation
- 2.1 Exponent Functions
- 2.2 The Modular
- 2.3 The Space Lp(.)( )
- 2.4 Hölder's Inequality and the Associate Norm
- 2.5 Embedding Theorems
- 2.6 Convergence in Lp(.)( )
- 2.7 Completeness and Dense Subsets of Lp(.)( )
- 2.8 The Dual Space of a Variable Lebesgue Space
- 2.9 The Lebesgue Differentiation Theorem
- 2.10 Notes and Further Results
- 3.1 Basic Properties
- 3.2 The Calderón-Zygmund Decomposition
- 3.3 The Maximal Operator on Variable Lebesgue Spaces
- 3.4 The Proof of Theorem 3.16
- 3.5 Modular Inequalities
- 3.6 Interpolation and Convexity
- 3.7 Notes and Further Remarks
- 4.1 Control at Infinity: The N Condition
- 4.2 A Useful Tool: Muckenhoupt Ap Weights
- 4.3 Applications of Weights to the Maximal Operator
- 4.4 Local Control: The K0 Condition
- 4.5 A Necessary and Sufficient Condition
- 4.6 Notes and Further Results
- 5.1 Basic Properties of Convolutions
- 5.2 Approximate Identities on Variable Lebesgue Spaces
- 5.3 The Failure of Young's Inequality
- 5.4 Rubio de Francia Extrapolation
- 5.5 Applications of Extrapolation
- 5.6 Notes and Further Results
- 6.1 The Space Wk, p(.)( )
- 6.2 Density of Smooth Functions
- 6.3 The Poincaré Inequalities
- 6.4 Sobolev Embedding Theorems
- 6.5 Notes and Further Results