On Necessary and Sufficient Conditions for Lp-Estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates - Couverture souple

Auscher, Pascal

Couverture souple

ISBN 10 : 0821839411 ISBN 13 : 9780821839416

Editeur : American Mathematical Society, 2007

Synopsis

This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p<2$ already treated earlier is radically different from the case $p>2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p<2$ and the other for $p>2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2007
• Langue: anglais
• ISBN 10: 0821839411
• ISBN 13: 9780821839416
• Reliure: Broché
• Nombre de pages: 75
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible