Fractional Sobolev inequalities: symmetrization, isoperimetry and interpolation
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
2014
|
| Schriftenreihe: | Astérisque
366 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [121] - 127 |
| Beschreibung: | VIII, 127 S. |
| ISBN: | 9782856297964 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Fractional Sobolev inequalities
Autor: Martín, Joaquim
Jahr: 2014
CONTENTS Preface ........................................................................ ix 1. Introduction ............................................................... 1 2. Preliminaries .............................................................. 15 2.1. Background ............................................................. 15 2.2. Rearrangement invariant spaces ......................................... 17 2.3. Some remarks about Sobolev spaces ..................................... 21 3. Oscillations, K-functionals and Isoperimetry .......................... 25 3.1. Summary ................................................................ 25 3.2. Estimation of the oscillation in terms of K —functionals ................. 25 3.3. A variant of Theorem 7 ................................................. 37 3.4. Isoperimetry ............................................................. 40 4. Embedding into continuous functions .................................. 43 4.1. Introduction and Summary .............................................. 43 4.2. Continuity via rearrangement inequalities ............................... 45 5. Examples and Applications .............................................. 51 5.1. Summary ................................................................ 51 5.2. Euclidean domains ...................................................... 51 5.3. Domains of Maz’ya’s class J a (1 — 1/n a 1) ........................ 59 5.4. Ahlfors Regular Metric Measure Spaces ................................. 61 6. Fractional Sobolev inequalities in Gaussian measures ................ 65 6.1. Introduction and Summary .............................................. 65 6.2. Boundedness of functions in Gaussian-Sobolev spaces ................... 66 6.3. Embeddings of Gaussian Besov spaces ................................... 68 6.4. Exponential Classes .............................................. 72
viii CONTENTS 7. On limiting Sobolev embeddings and BMO ............................ 75 7.1. Introduction and Summary .............................................. 75 7.2. On the John-Stromberg characterization of BMO ....................... 80 7.3. Oscillation, BMO and if—functionals ................................... 82 8. Estimation of growth “envelopes” ....................................... 85 8.1. Summary ................................................................ 85 8.2. Spaces defined on measure spaces with Euclidean type profile ........... 86 8.3. Continuity Envelopes .................................................... 92 8.4. General isoperimetric profiles ............................................ 93 8.5. Envelopes for higher order spaces ..................... 95 8.6. K and E functionals for families ........................................ 97 9. Lorentz spaces with negative indices ................................... 99 9.1. Introduction and Summary .............................................. 99 9.2. The role of the L^ ,p 1 spaces in Morrey’s theorem ........................100 9.3. An interpolation inequality ..............................................102 ; 9.4. Further remarks .........................................................103 10. Connection with the work of Garsia and his collaborators .........105 A. Some remarks on the calculation of AT—functionals ..................113 A.l. Introduction ............................................................113 A.2. Semigroups and Interpolation ...........................................115 A.3. Specific Semigroups .....................................................119 Bibliography ..................................................................121 ASTÉRISQUE 366
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| author | Martín, Joaquim Milman, Mario 1950- |
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| ctrlnum | (OCoLC)902844827 (DE-599)GBV817038892 |
| discipline | Mathematik |
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| id | DE-604.BV042325729 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:29Z |
| institution | BVB |
| isbn | 9782856297964 |
| language | English |
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| physical | VIII, 127 S. |
| publishDate | 2014 |
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| series | Astérisque |
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| spelling | Martín, Joaquim Verfasser (DE-588)1066273251 aut Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Joaquim Martín ; Mario Milman Paris Soc. Math. de France 2014 VIII, 127 S. txt rdacontent n rdamedia nc rdacarrier Astérisque 366 Literaturverz. S. [121] - 127 Zs.fassung in franz. Sprache Milman, Mario 1950- Verfasser (DE-588)1066585695 aut Astérisque 366 (DE-604)BV002579439 366 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027762570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martín, Joaquim Milman, Mario 1950- Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Astérisque |
| title | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation |
| title_auth | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation |
| title_exact_search | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation |
| title_full | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Joaquim Martín ; Mario Milman |
| title_fullStr | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Joaquim Martín ; Mario Milman |
| title_full_unstemmed | Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Joaquim Martín ; Mario Milman |
| title_short | Fractional Sobolev inequalities |
| title_sort | fractional sobolev inequalities symmetrization isoperimetry and interpolation |
| title_sub | symmetrization, isoperimetry and interpolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027762570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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