Comptes Rendus
Harmonic analysis
Sharp weighted estimates involving one supremum
[Estimations pondérées précisées associées à un seul supremum]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 906-909.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.07.016

Kangwei Li 1

1 BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain
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Kangwei Li. Sharp weighted estimates involving one supremum. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 906-909. doi : 10.1016/j.crma.2017.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.016/

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

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

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

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

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

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

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

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

[9] M.T. Lacey An elementary proof of the A2 bound, Isr. J. Math., Volume 217 (2017), pp. 181-195

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

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

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

[13] A.K. Lerner; K. Moen Mixed ApA estimates with one supremum, Stud. Math., Volume 219 (2013) no. 3, pp. 247-267

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

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

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

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