Lebesgue and Sobolev spaces with variable exponents:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture notes in mathematics
2017 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 509 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 364218362X 9783642183621 |
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MARC
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| 245 | 1 | 0 | |a Lebesgue and Sobolev spaces with variable exponents |c Lars Diening ... |
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| 490 | 1 | |a Lecture notes in mathematics |v 2017 | |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 HISTORY OF VARIABLE EXPONENT SPACES 2
1.2 STRUCTURE OF THE BOOK 4
1.3 SUMMARY OF CENTRAL RESULTS 7
1.4 NOTATION AND BACKGROUND 10
PART I LEBESGUE SPACES
2 A FRAMEWORK FOR FUNCTION SPACES 21
2.1 BASIC PROPERTIES OF SEMIMODULAR SPACES 21
2.2 CONJUGATE MODULARS AND DUAL SEMIMODULAR SPACES 29 2.3
MUSIELAK-ORLICZ SPACES: BASIC PROPERTIES 34
2.4 UNIFORM CONVEXITY 42
2.5 SEPARABILITY 48
2.6 CONJUGATE ^-FUNCTIONS 52
2.7 ASSOCIATE SPACES AND DUAL SPACES 57
2.8 EMBEDDINGS AND OPERATORS 66
3 VARIABLE EXPONENT LEBESGUE SPACES 69
3.1 THE LEBESGUE SPACE ^-FUNCTION 69
3.2 BASIC PROPERTIES 73
3.3 EMBEDDINGS 82
3.4 PROPERTIES FOR RESTRICTED EXPONENTS 87
3.5 LIMIT OF EXPONENTS 92
3.6 CONVOLUTION* 94
4 THE MAXIMAL OPERATOR 99
4.1 LOGARITHMIC HOLDER CONTINUITY 100
4.2 POINT-WISE ESTIMATES 104
4.3 THE BOUNDEDNESS OF THE MAXIMAL OPERATOR 110
4.4 WEAK-TYPE ESTIMATES AND AVERAGING OPERATORS 115
4.5 NORMS OF CHARACTERISTIC FUNCTIONS 122
4.6 MOLLIFICATION AND CONVOLUTION 127
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009117831
DIGITALISIERT DURCH
IMAGE 2
VIN CONTENTS
4.7 NECESSARY CONDITIONS FOR BOUNDEDNESS* 131
4.8 PREIMAGE OF THE MAXIMAL OPERATOR* 138
5 THE GENERALIZED MUCKENHOUPT CONDITION* 143
5.1 NON SUFFICIENCY OF LOG-HOELDER CONTINUITY* 143
5.2 CLASS A * 149
5.3 CLASS A FOR VARIABLE EXPONENT LEBESGUE SPACES* 157 5.4 CLASS ^OO*
159
5.5 A SUFFICIENT CONDITION FOR THE BOUNDEDNESS OF M * 168 5.6
CHARACTERIZATION OF (STRONG-)DOMINATION* 175
5.7 THE CASE OF LEBESGUE SPACES WITH VARIABLE EXPONENTS* 180 5.8
WEIGHTED VARIABLE EXPONENT LEBESGUE SPACES* 192
6 CLASSICAL OPERATORS 199
6.1 RIESZ POTENTIALS 199
6.2 THE SHARP OPERATOR M"/ 206
6.3 CALDEROEN-ZYGMUND OPERATORS 208
7 TRANSFER TECHNIQUES 213
7.1 COMPLEX INTERPOLATION 213
7.2 EXTRAPOLATION RESULTS 218
7.3 LOCAL-TO-GLOBAL RESULTS 222
7.4 BALL/CUBES-TO-JOHN 237
PART II SOBOLEV SPACES
8 INTRODUCTION TO SOBOLEV SPACES 247
8.1 BASIC PROPERTIES 247
8.2 POINCARE INEQUALITIES 252
8.3 SOBOLEV-POINCARE INEQUALITIES AND EMBEDDINGS 265 8.4 COMPACT
EMBEDDINGS 272
8.5 EXTENSION OPERATOR 275
8.6 LIMITING CASES OF SOBOLEV EMBEDDINGS* 283
9 DENSITY OF REGULAR FUNCTIONS 289
9.1 BASIC RESULTS ON DENSITY 290
9.2 DENSITY WITH CONTINUOUS EXPONENTS 293
9.3 DENSITY WITH DISCONTINUOUS EXPONENTS* 299
9.4 DENSITY OF CONTINUOUS FUNCTIONS* 305
9.5 THE LIPSCHITZ TRUNCATION METHOD* 310
10 CAPACITIES 315
10.1 SOBOLEV CAPACITY 315
10.2 RELATIVE CAPACITY 322
10.3 THE RELATIONSHIP BETWEEN THE CAPACITIES 331
10.4 SOBOLEV CAPACITY AND HAUSDORFT MEASURE 334
IMAGE 3
CONTENTS IX
11 FINE PROPERTIES OF SOBOLEV FUNCTIONS 339
11.1 QUASICONTINUITY 339
11.2 SOBOLEV SPACES WITH ZERO BOUNDARY VALUES 345
11.3 EXCEPTIONAL SETS IN VARIABLE EXPONENT SOBOLEV SPACES 350 11.4
LEBESGUE POINTS 352
11.5 FAILURE OF EXISTENCE OF LEBESGUE POINTS* 360
12 OTHER SPACES OF DIFFERENTIABLE FUNCTIONS 367
12.1 TRACE SPACES 368
12.2 HOMOGENEOUS SOBOLEV SPACES 378
12.3 SOBOLEV SPACES WITH NEGATIVE SMOOTHNESS 383
12.4 BESSEL POTENTIAL SPACES* 388
12.5 BESOV AND TRIEBEL-LIZORKIN SPACES* 392
PART III APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS
13 DIRICHLET ENERGY INTEGRAL AND LAPLACE EQUATION 401
13.1 THE ONE DIMENSIONAL CASE 402
13.2 MINIMIZERS 412
13.3 HARMONIC AND SUPERHARMONIC FUNCTIONS 417
13.4 HARNACK'S INEQUALITY FOR A-HARMONIC FUNCTIONS 421
14 P D ES AND FLUID DYNAMICS 437
14.1 POISSON PROBLEM 437
14.2 STOKES PROBLEM 446
14.3 DIVERGENCE EQUATION AND CONSEQUENCES 459
14.4 ELECTRORHEOLOGICAL FLUIDS 470
REFERENCES 483
LIST OF SYMBOLS 501
INDEX 505 |
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV037387733 |
| classification_rvk | SI 850 SK 600 |
| classification_tum | MAT 464f MAT 350f |
| ctrlnum | (OCoLC)723554139 (DE-599)DNB1009117831 |
| dewey-full | 515.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
| dewey-search | 515.73 |
| dewey-sort | 3515.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 364218362X 9783642183621 |
| language | English |
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| physical | IX, 509 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2011 |
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| spelling | Lebesgue and Sobolev spaces with variable exponents Lars Diening ... Berlin [u.a.] Springer 2011 IX, 509 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2017 Lp-Raum (DE-588)4168195-2 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s Lp-Raum (DE-588)4168195-2 s DE-604 Diening, Lars Sonstige oth Erscheint auch als Online-Ausgabe 978-3-642-18363-8 Lecture notes in mathematics 2017 (DE-604)BV000676446 2017 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3639527&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022540701&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lebesgue and Sobolev spaces with variable exponents Lecture notes in mathematics Lp-Raum (DE-588)4168195-2 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4168195-2 (DE-588)4055345-0 |
| title | Lebesgue and Sobolev spaces with variable exponents |
| title_auth | Lebesgue and Sobolev spaces with variable exponents |
| title_exact_search | Lebesgue and Sobolev spaces with variable exponents |
| title_full | Lebesgue and Sobolev spaces with variable exponents Lars Diening ... |
| title_fullStr | Lebesgue and Sobolev spaces with variable exponents Lars Diening ... |
| title_full_unstemmed | Lebesgue and Sobolev spaces with variable exponents Lars Diening ... |
| title_short | Lebesgue and Sobolev spaces with variable exponents |
| title_sort | lebesgue and sobolev spaces with variable exponents |
| topic | Lp-Raum (DE-588)4168195-2 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Lp-Raum Sobolev-Raum |
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