Bellman function and bilinear embedding theorem for Schrödinger-type operators

Oliver Dragičević; Alexander Volberg

doi:10.1016/j.crma.2009.02.004

Harmonic Analysis/Functional Analysis

Bellman function and bilinear embedding theorem for Schrödinger-type operators
[Fonction de Bellman et le plongement bilinéaire pour des opérateurs de Schrödinger]

Présenté par : Gilles Pisier

Oliver Dragičević ¹ ; Alexander Volberg ^2,³

¹ Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
³ School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK

Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 537-540.

Résumé
Abstract

On considère un théorème de plongement bilinéaire pour une classe des opérateurs de Schrödinger sur $L^{p}$ . Le résultat ne depend pas de dimension et il est p-linéaire. On fait une esquisse de la démonstration basée sur trois observations concernant la fonction de Bellman spécifique.

We discuss bilinear embedding theorems for a certain class of Schrödinger operators on $L^{p}$ . The obtained estimates are dimension-free and linear in p. We outline a uniform proof of the theorem which relies on establishing three crucial properties of the concrete Bellman function we consider.

Reçu le : 2009-01-26
Accepté le : 2009-01-27
Publié le : 2009-03-13

DOI : 10.1016/j.crma.2009.02.004

Affiliations des auteurs :

Oliver Dragičević ¹ ; Alexander Volberg ^{2, 3}

¹ Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
³ School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK

@article{CRMATH_2009__347_9-10_537_0,
     author = {Oliver Dragi\v{c}evi\'c and Alexander Volberg},
     title = {Bellman function and bilinear embedding theorem for {Schr\"odinger-type} operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {537--540},
     publisher = {Elsevier},
     volume = {347},
     number = {9-10},
     year = {2009},
     doi = {10.1016/j.crma.2009.02.004},
     language = {en},
}

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%A Alexander Volberg
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Oliver Dragičević; Alexander Volberg. Bellman function and bilinear embedding theorem for Schrödinger-type operators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 537-540. doi : 10.1016/j.crma.2009.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.004/

Bibliographie
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