Harmonic analysis
Sharp weighted estimates involving one supremum
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 906-909.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.016
Li, Kangwei 1

1 BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain
@article{CRMATH_2017__355_8_906_0,
     author = {Li, Kangwei},
     title = {Sharp weighted estimates involving one supremum},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {906--909},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.016},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.07.016/}
}
TY  - JOUR
AU  - Li, Kangwei
TI  - Sharp weighted estimates involving one supremum
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 906
EP  - 909
VL  - 355
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.07.016/
DO  - 10.1016/j.crma.2017.07.016
LA  - en
ID  - CRMATH_2017__355_8_906_0
ER  - 
%0 Journal Article
%A Li, Kangwei
%T Sharp weighted estimates involving one supremum
%J Comptes Rendus. Mathématique
%D 2017
%P 906-909
%V 355
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.07.016/
%R 10.1016/j.crma.2017.07.016
%G en
%F CRMATH_2017__355_8_906_0
Li, Kangwei. 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. http://www.numdam.org/articles/10.1016/j.crma.2017.07.016/

[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 ApA 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, 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 A2 bound, Isr. J. Math., Volume 217 (2017), pp. 181-195

[10] Lerner, A.K. Mixed ApAr 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 ApA 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

Cited by Sources: