| Title:
|
On the weighted estimate of the Bergman projection (English) |
| Author:
|
Sehba, Benoît Florent |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
497-511 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given. (English) |
| Keyword:
|
Bergman space |
| Keyword:
|
reproducing kernel |
| Keyword:
|
Toeplitz operator |
| Keyword:
|
Békollé-Bonami weight |
| MSC:
|
30H20 |
| MSC:
|
42A61 |
| MSC:
|
42C40 |
| MSC:
|
47B35 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 06890386 |
| idMR:
|
MR3819187 |
| DOI:
|
10.21136/CMJ.2018.0531-16 |
| . |
| Date available:
|
2018-06-11T10:56:27Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147232 |
| . |
| Reference:
|
[1] Aleman, A., Pott, S., Reguera, M. C.: Sarason conjecture on the Bergman space.Int. Math. Res. Not. 2017 (2017), 4320-4349. MR 3674172, 10.1093/imrn/rnw134 |
| Reference:
|
[2] Bekollé, D.: Inégalité à poids pour le projecteur de Bergman dans la boule unité de $\mathbb C^n$.Stud. Math. 71 (1982), 305-323 French. Zbl 0516.47016, MR 0667319, 10.4064/sm-71-3-305-323 |
| Reference:
|
[3] Bekollé, D., Bonami, A.: Inégalités à poids pour le noyau de Bergman.C. R. Acad. Sci., Paris, Sér. A 286 (1978), 775-778 French. Zbl 0398.30006, MR 0497663 |
| Reference:
|
[4] Cruz-Uribe, D.: The invertibility of the product of unbounded Toeplitz operators.Integral Equations Oper. Theory 20 (1994), 231-237. Zbl 0817.47034, MR 1294717, 10.1007/BF01679672 |
| Reference:
|
[5] García-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies, 116 Notas de Matemática (104), North-Holland Publishing, Amsterdam (1985). Zbl 0578.46046, MR 0807149, 10.1016/s0304-0208(08)x7154-3 |
| Reference:
|
[6] Hytönen, T. P., Lacey, M. T., Pérez, C.: Sharp weighted bounds for the $q$-variation of singular integrals.Bull. Lond. Math. Soc. 45 (2013), 529-540. Zbl 1271.42021, MR 3065022, 10.1112/blms/bds114 |
| Reference:
|
[7] Hytönen, T., Pérez, C.: Sharp weighted bounds involving $A_{\infty}$.Anal. PDE 6 (2013), 777-818. Zbl 1283.42032, MR 3092729, 10.2140/apde.2013.6.777 |
| Reference:
|
[8] Isralowitz, J.: Invertible Toeplitz products, weighted norm inequalities, and $ A_p$ weights.J. Oper. Theory 71 (2014), 381-410. Zbl 1313.47059, MR 3214643, 10.7900/jot.2012apr10.1989 |
| Reference:
|
[9] Lerner, A. K.: A simple proof of the $A_2$ conjecture.Int. Math. Res. Not. 2013 (2013), 3159-3170. Zbl 1318.42018, MR 3085756, 10.1093/imrn/rns145 |
| Reference:
|
[10] Michalska, M., Nowak, M., Sobolewski, P.: Bounded Toeplitz and Hankel products on weighted Bergman spaces of the unit ball.Ann. Pol. Math. 99 (2010), 45-53. Zbl 1239.47021, MR 2660591, 10.4064/ap99-1-4 |
| Reference:
|
[11] Moen, K.: Sharp weighted bounds without testing or extrapolation.Arch. Math. 99 (2012), 457-466. Zbl 1266.42037, MR 3000426, 10.1007/s00013-012-0453-4 |
| Reference:
|
[12] Nazarov, F.: A counterexample to Sarason's conjecture.Preprint available at\ http://users.math.msu.edu/users/fedja/Preprints/Sarps.html. |
| Reference:
|
[13] Pott, S., Reguera, M. C.: Sharp Békollé estimates for the Bergman projection.J. Funct. Anal. 265 (2013), 3233-3244. Zbl 1295.46020, MR 3110501, 10.1016/j.jfa.2013.08.018 |
| Reference:
|
[14] Pott, S., Strouse, E.: Products of Toeplitz operators on the Bergman spaces $A^2_\alpha$.Algebra Anal. 18 (2006), 144-161 translation in St. Petersbg. Math. J. 18 2007 105-118. Zbl 1127.47028, MR 2225216, 10.1090/S1061-0022-06-00945-9 |
| Reference:
|
[15] Sarason, D.: Products of Toeplitz operators.Linear and Complex Analysis Problem Book 3, Part I V. P. Havin, N. K. Nikolski Lecture Notes in Mathematics 1573, Springer, Berlin (1994), 318-319. Zbl 0893.30036, MR 1334345, 10.1007/BFb0100201 |
| Reference:
|
[16] Stroethoff, K., Zheng, D.: Bounded Toeplitz products on the Bergman space of the polydisk.J. Math. Anal. Appl. 278 (2003), 125-135. Zbl 1051.47025, MR 1963469, 10.1016/S0022-247X(02)00578-4 |
| Reference:
|
[17] Stroethoff, K., Zheng, D.: Bounded Toeplitz products on Bergman spaces of the unit ball.J. Math. Anal. Appl. 325 (2007), 114-129. Zbl 1111.32003, MR 2273032, 10.1016/j.jmaa.2006.01.009 |
| Reference:
|
[18] Stroethoff, K., Zheng, D.: Bounded Toeplitz products on weighted Bergman spaces.J. Oper. Theory 59 (2008), 277-308. Zbl 1199.47127, MR 2411047 |
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