A note on weighted bounds for rough singular integrals

Andrei K. Lerner

doi:10.1016/j.crma.2017.11.016

Harmonic analysis

A note on weighted bounds for rough singular integrals

Presented by: the Editorial Board

Andrei K. Lerner ¹

¹ Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel

Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 77-80.

Abstract
Résumé

We show that the $L^{2} (w)$ operator norm of the composition $M \circ T_{Ω}$ , where M is the maximal operator and $T_{Ω}$ is a rough homogeneous singular integral with angular part $Ω \in L^{\infty} (S^{n - 1})$ , depends quadratically on ${[w]}_{A_{2}}$ , and that this dependence is sharp.

Nous montrons que la norme d'opérateur $L^{2} (w)$ du composé $M \circ T_{Ω}$ , où M est l'opérateur maximal et $T_{Ω}$ est une intégrale singulière homogène rugueuse de partie angulaire $Ω \in L^{\infty} (S^{n - 1})$ , dépend de manière quadratique de ${[w]}_{A_{2}}$ et que cette dépendance est précise.

Received: 2017-09-27
Accepted: 2017-11-24
Published online: 2017-12-08

DOI: 10.1016/j.crma.2017.11.016

Author's affiliations:

Andrei K. Lerner ¹

¹ Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel

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Andrei K. Lerner. A note on weighted bounds for rough singular integrals. Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 77-80. doi : 10.1016/j.crma.2017.11.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.11.016/

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