Variable lebesgue spaces foundations and harmonic analysis
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Basel [u.a.]
Springer
2013
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| Schriftenreihe: | Applied and numerical harmonic analysis
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| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
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| 100 | 1 | |a Cruz-Uribe, David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Variable lebesgue spaces |b foundations and harmonic analysis |c David V. Cruz-Uribe ; Alberto Fiorenza |
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 1920912 |
|---|---|
| _version_ | 1816713861918621696 |
| adam_text | VARIABLE LEBESGUE SPACES
/ CRUZ-URIBE, DAVID V.
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1 INTRODUCTION
2 STRUCTURE OF VARIABLE LEBESGUE SPACES
3 THE HARDY-LITTLEWOOD MAXIMAL OPERATOR.-4 BEYOND LOG-HOELDER
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
VARIABLE LEBESGUE SPACES
/ CRUZ-URIBE, DAVID V.
: 2013
ABSTRACT / INHALTSTEXT
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 LEBESGUESPACES 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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Cruz-Uribe, David Fiorenza, Alberto |
| author_facet | Cruz-Uribe, David Fiorenza, Alberto |
| author_role | aut aut |
| author_sort | Cruz-Uribe, David |
| author_variant | d c u dcu a f af |
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| bvnumber | BV040913564 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)1074267181 (DE-599)DNB1031500707 |
| dewey-full | 515.785 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.785 |
| dewey-search | 515.785 |
| dewey-sort | 3515.785 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0548-3 |
| format | Electronic eBook |
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| id | DE-604.BV040913564 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:37:10Z |
| institution | BVB |
| isbn | 9783034805476 9783034805483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025892847 |
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| series2 | Applied and numerical harmonic analysis |
| spellingShingle | Cruz-Uribe, David Fiorenza, Alberto Variable lebesgue spaces foundations and harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4034949-4 |
| title | Variable lebesgue spaces foundations and harmonic analysis |
| title_auth | Variable lebesgue spaces foundations and harmonic analysis |
| title_exact_search | Variable lebesgue spaces foundations and harmonic analysis |
| title_full | Variable lebesgue spaces foundations and harmonic analysis David V. Cruz-Uribe ; Alberto Fiorenza |
| title_fullStr | Variable lebesgue spaces foundations and harmonic analysis David V. Cruz-Uribe ; Alberto Fiorenza |
| title_full_unstemmed | Variable lebesgue spaces foundations and harmonic analysis David V. Cruz-Uribe ; Alberto Fiorenza |
| title_short | Variable lebesgue spaces |
| title_sort | variable lebesgue spaces foundations and harmonic analysis |
| title_sub | foundations and harmonic analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Harmonische Analyse Lebesgue-Integral |
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