Sharp weighted estimates involving one supremum

Li, Kangwei

doi:10.1016/j.crma.2017.07.016

Harmonic analysis

Sharp weighted estimates involving one supremum
[Estimations pondérées précisées associées à un seul supremum]

Présenté par : the Editorial Board

Li, Kangwei ¹

¹ BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain

Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 906-909.

Résumé
Abstract

Nous étudions dans cette note les estimations pondérées précisées associées à un seul supremum. En particulier, nous résolvons par l'affirmative un probléme ouvert posé par Lerner et Moen. Nous étendons également le résultat aux opérateurs intégraux singuliers homogènes rugueux.

In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular integral operators.

Reçu le : 2017-05-24
Accepté le : 2017-07-26
Publié le : 2017-08-01

DOI : 10.1016/j.crma.2017.07.016

Affiliations des auteurs :

Li, Kangwei ¹

¹ BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain

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Li, Kangwei. Sharp weighted estimates involving one supremum. Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 906-909. doi : 10.1016/j.crma.2017.07.016. http://www.numdam.org/articles/10.1016/j.crma.2017.07.016/

Bibliographie
Cité par

[1] Conde-Alonso, J.M.; Culiuc, A.; Di Plinio, F.; Ou, Y. A sparse domination principle for rough singular integrals, Anal. PDE, Volume 10 (2017) no. 5, pp. 1255-1284

[2] Conde-Alonso, J.M.; Rey, G. A pointwise estimate for positive dyadic shifts and some applications, Math. Ann., Volume 365 (2016), pp. 1111-1135

[3] Duoandikoetxea, J. Extrapolation of weights revisited: new proofs and sharp bounds, J. Funct. Anal., Volume 260 (2011), pp. 1886-1901

[4] Duoandikoetxea, J.; Rubio de Francia, J.L. Maximal and singular integral operators via Fourier transform estimates, Invent. Math., Volume 84 (1986), pp. 541-561

[5] Hytönen, T.P. The sharp weighted bound for general Calderón–Zygmund operators, Ann. of Math. (2), Volume 175 (2012) no. 3, pp. 1473-1506

[6] Hytönen, T.P.; Lacey, M.T. The $A_{p}$ – $A_{\infty}$ inequality for general Calderón–Zygmund operators, Indiana Univ. Math. J., Volume 61 (2012) no. 6, pp. 2041-2092

[7] Hytönen, T.P.; Pérez, C. Sharp weighted bounds involving $A_{\infty}$ , Anal. PDE, Volume 6 (2013) no. 4, pp. 777-818

[8] Hytönen, T.P.; Roncal, L.; Tapiola, O. Quantitative weighted estimates for rough homogeneous singular integrals, Isr. J. Math., Volume 218 (2017), pp. 133-164

[9] Lacey, M.T. An elementary proof of the $A_{2}$ bound, Isr. J. Math., Volume 217 (2017), pp. 181-195

[10] Lerner, A.K. Mixed $A_{p}$ – $A_{r}$ inequalities for classical singular integrals and Littlewood–Paley operators, J. Geom. Anal., Volume 23 (2013) no. 3, pp. 1343-1354

[11] Lerner, A.K. On pointwise estimates involving sparse operators, N.Y. J. Math., Volume 22 (2016), pp. 341-349

[12] Lerner, A.K. A weak type estimate for rough singular integrals (preprint, available at) | arXiv

[13] Lerner, A.K.; Moen, K. Mixed $A_{p}$ – $A_{\infty}$ estimates with one supremum, Stud. Math., Volume 219 (2013) no. 3, pp. 247-267

[14] Lerner, A.K.; Nazarov, F. Intuitive dyadic calculus: the basics, 2015 (preprint, available at) | arXiv

[15] Li, K. Two weight inequalities for bilinear forms, Collect. Math., Volume 68 (2017), pp. 129-144

[16] Li, K.; Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. Weighted norm inequalities for rough singular integral operators (preprint, available at) | arXiv

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