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20140310151453.0 |
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130217s2013 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9783034805483 |
|
978-3-0348-0548-3 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA403-403.3 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.785 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Basel : |
| -- |
Springer Basel : |
| -- |
Imprint: Birkhäuser, |
| -- |
2013. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Cruz-Uribe, David V. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Variable Lebesgue Spaces |
| Medium |
[electronic resource] : |
| Remainder of title |
Foundations and Harmonic Analysis / |
| Statement of responsibility, etc |
by David V. Cruz-Uribe, Alberto Fiorenza. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
IX, 312 p. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Applied and Numerical Harmonic Analysis |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. . |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Harmonic analysis. |
|
|---|
| Topical term or geographic name as entry element |
Functional analysis. |
|
|---|
| Topical term or geographic name as entry element |
Global analysis. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Abstract Harmonic Analysis. |
|
|---|
| Topical term or geographic name as entry element |
Functional Analysis. |
|
|---|
| Topical term or geographic name as entry element |
Global Analysis and Analysis on Manifolds. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Fiorenza, Alberto. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783034805476 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-0348-0548-3 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
