A new weighted Bellman function

Pattakos, Nikolaos; Volberg, Alexander

doi:10.1016/j.crma.2011.10.007

Mathematical Analysis/Harmonic Analysis

A new weighted Bellman function
[Une nouvelle fonction pondérée de Bellman]

Présenté par : Gilles Pisier

Pattakos, Nikolaos ¹ ; Volberg, Alexander ¹

¹ Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1151-1154.

Résumé
Abstract

Nous construisons une nouvelle fonction de Bellman qui nous permet de donner des estimations précises de la norme des transformées de Riesz dans les espaces pondérés $L^{p} (w d x)$ , quand la caractéristique du poids est proche de 1.

We give sharp in p and w estimates of operator norms of Riesz transforms in the $L^{p} (w d x)$ spaces, when the $A_{p}$ characteristic of the weight is close to 1 (flat case). This is done by proving the existence of a certain Bellman function.

Reçu le : 2011-05-19
Accepté le : 2011-10-10
Publié le : 2011-10-22

DOI : 10.1016/j.crma.2011.10.007

Affiliations des auteurs :

Pattakos, Nikolaos ¹ ; Volberg, Alexander ¹

¹ Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

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     title = {A new weighted {Bellman} function},
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Pattakos, Nikolaos; Volberg, Alexander. A new weighted Bellman function. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1151-1154. doi : 10.1016/j.crma.2011.10.007. https://www.numdam.org/articles/10.1016/j.crma.2011.10.007/

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