On a discrete bilinear singular operator

Dong Dong

doi:10.1016/j.crma.2017.03.010

Harmonic analysis

On a discrete bilinear singular operator
[Sur un opérateur bilinéaire discret singulier]

Présenté par : Yves Meyer

Dong Dong ¹

¹ Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green Street, Urbana, IL 61801, USA

Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 538-542.

Résumé
Abstract

Nous montrons, que pour une grande classe de fonctions P et Q, l'opérateur bilinéaire discret $T_{P, Q} (f, g) (n) = \sum_{m \in Z ∖ {0}} f (n - P (m)) g (n - Q (m)) \frac{1}{m}$ est borné de $l^{2} \times l^{2}$ dans $l^{1 + ϵ, \infty}$ , pour tout $ϵ \in (0, 1]$ .

We prove that for a large class of functions P and Q, the discrete bilinear operator $T_{P, Q} (f, g) (n) = \sum_{m \in Z ∖ {0}} f (n - P (m)) g (n - Q (m)) \frac{1}{m}$ is bounded from $l^{2} \times l^{2}$ into $l^{1 + ϵ, \infty}$ for any $ϵ \in (0, 1]$ .

Reçu le : 2016-09-27
Accepté le : 2017-03-15
Publié le : 2017-03-29

DOI : 10.1016/j.crma.2017.03.010

Affiliations des auteurs :

Dong Dong ¹

¹ Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green Street, Urbana, IL 61801, USA

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Dong Dong. On a discrete bilinear singular operator. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 538-542. doi : 10.1016/j.crma.2017.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.03.010/

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