Abstract
We characterize bounded and invertible Toeplitz products on vector weighted Bergman spaces of the unit polydisc. For our purpose, we will need the notion of Békollé–Bonami weights in several parameters.
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Aleman, A., Pott, S., Reguera, M.C.: Sarason conjecture on Bergman space. arXiv:1304.1750. To appear in Intern. Math. Res. Notices
Békollé, D.:Inégalités à poids pour le project de Bergman dans la boule unité de \({\mathbb{C}}^n\). Weighted inequalities for the Bergman projection in the unit ball of Cn. Stud. Math. 71(3), 305–323 (1981/82) (French)
Békollé, D., Bonami, A.: Inégalités à poids pour le noyau de Bergman. Weighted inequalities for the Bergman kernel. C. R. Acad. Sci. Paris Sér. A–B 286(18), A775–A778 (1978) (French)
Isralowitz, J.: Invertible Toeplitz products, weighted inequalities and \(A_p\) weights. J. Oper. Theor. 71(2), 381–410 (2014)
Lu, Y., Sun, Z.: Invertible Toeplitz operators products on the Bergman spaces of the polydisc. J. Math. Res. Appl. Sept. 32(5), 543–553 (2012)
Miao, J.: Bounded Toeplitz products on the weighted Bergman spaces of the unit ball. J. Math. Anal. Appl. 346, 305–313 (2008)
Pott, S., Reguera, M.C.: Sharp Békollé estimates for the Bergman projection. J. Funct. Anal. 265, 3233–3244 (2013)
Stroethoff, K., Zheng, A.D.: Invertible Toeplitz products. J. Funct. Anal. 195(1), 48–70 (2002)
Stroethoff, K., Zheng, A.D.: Bounded Toeplitz products on the Bergman space of the polydisk. J. Math. Anal. Appl. 278(1), 125–135 (2003)
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Sehba, B.F. Bounded and Invertible Toeplitz Products on Vector Weighted Bergman Spaces of the Unit Polydisc. Mediterr. J. Math. 14, 178 (2017). https://doi.org/10.1007/s00009-017-0978-7
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DOI: https://doi.org/10.1007/s00009-017-0978-7