1.

Record Nr.

UNINA9910828649203321

Autore

Auscher Pascal

Titolo

On necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on Rn and related estimates / / Pascal Auscher

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 2007

©2007

ISBN

1-4704-0475-3

Descrizione fisica

1 online resource (102 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 186, Number 871

Classificazione

31.46

Disciplina

515/.23

Soggetti

Singular integrals

Littlewood-Paley theory

Calderón-Zygmund operator

Elliptic operators

Semigroups

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 186, Number 871 (first of five numbers)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""Contents""; ""Acknowledgements""; ""Introduction""; ""Notation""; ""Chapter 1. Beyond Caldero'n-Zygmund operators""; ""Chapter 2. Basic L[sup(2)] theory for elliptic operators""; ""2.1. Definition""; ""2.2. Holomorphic functional calculus on L[sup(2)]""; ""2.3. L[sup(2)] off-diagonal estimates""; ""2.4. Square root""; ""2.5. The conservation property""; ""Chapter 3. L[sup(P)] theory for the semigroup""; ""3.1. Hypercontr activity and uniform boundedness""; ""3.2. W[sup(1,p)] elliptic estimates and hypercontr activity""; ""3.3. Gradient estimates""; ""3.4. Summary""

""3.5. Sharpness issues""""3.6. Analytic extension""; ""Chapter 4. L[sup(p)]  theory for square roots""; ""4.1. Riesz transforms on L[sup(p)]""; ""4.2. Reverse inequalities""; ""4.3. Invertibility""; ""4.4. Applications""; ""4.5. Riesz transforms and Hodge decomposition""; ""Chapter 5. Riesz transforms and functional calculi""; ""5.1. Blunck & Kunstmann's theorem""; ""5.2. Hardy-Littlewood-Sobolev estimates""; ""5.3. The Hardy-Littlewood-Sobolev-Kato diagram""; ""5.4. More on the Kato



diagram""; ""Chapter 6. Square function estimates""

""6.1. Necessary and sufficient conditions for boundedness of vertical square functions""""6.2. On inequalities of Stein and Fefferman for non-tangential square functions""; ""Chapter 7. Miscellani""; ""7.1. Local theory""; ""7.2. Higher order operators and systems""; ""Appendix A. Calderon-Zygmund decomposition for Sobolev functions""; ""Appendix. Bibliography""