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...
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| Autori principali: | , |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Basel :
Springer Basel
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2013. |
| Serie: | Applied and Numerical Harmonic Analysis
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| Soggetti: | |
| Accesso online: | 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 |
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| 009 | PPN168307456 | ||
| 020 | |a 9783034805483 | ||
| 041 | 0 | |a eng | |
| 082 | |a 515.785 | ||
| 100 | 1 | |a Cruz-Uribe, David V. | |
| 245 | 1 | 0 | |a Variable Lebesgue spaces : |b foundations and harmonic analysis |c by David V. Cruz-Uribe, Alberto Fiorenza. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a Basel : |b Springer Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Applied and Numerical Harmonic Analysis |x 2296-5017 | |
| 500 | |a L'impression du document génère 315 p. | ||
| 500 | |a Collection de l'édition imprimée : "Applied and Numerical Harmonic Analysis" | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliographie p. 275-289. Index | ||
| 505 | 1 | |a 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. | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces. | ||
| 650 | |a Analyse fonctionnelle | ||
| 650 | |a Analyse harmonique (mathématiques) | ||
| 650 | |a Analyse globale (mathématiques) | ||
| 700 | 1 | |a Fiorenza, Alberto. |4 aut | |
| 776 | 0 | |0 175024634 |t Variable Lebesgue spaces |o foundations and harmonic analysis |f David V. Cruz-Uribe, Alberto Fiorenza |c Heidelberg |n Birkhäuser/Springer |d 2013 |p 1 vol. (IX - 312 p.) |s Applied and numerical harmonic analysis |z 978-3-0348-0547-6 | |
| 776 | 0 | |t Variable Lebesgue Spaces |b Texte imprimé |z 9783034805490 | |
| 776 | 0 | |t Variable Lebesgue Spaces |b Texte imprimé |z 9783034807579 | |
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| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-J348VBJ5-S |z Accès sur la plateforme Istex | |
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| 856 | 4 | |5 180339901:751539996 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-3-0348-0548-3 |z Accès INSA CVL | |
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