Geodesic
Products of Toeplitz and Hankel operators on the Bergman space in the polydisk
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 72 (2018) no. 2

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In this paper we obtain a condition for analytic square integrable functions f,g which guarantees the boundedness of products of the Toeplitz operators T_fT_g̅ densely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators H_fH^*_g is also given.
Keywords: Toeplitz operator, Bergman space 
Sobolewski, Paweł. Products of Toeplitz and Hankel operators on the Bergman space in the polydisk. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 72 (2018) no. 2. http://geodesic.mathdoc.fr/item/AUM_2018_72_2_a6/
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[1] Gonessa, J., Sheba, B., Toeplitz products on the vector weighted Bergman spaces, Acta Sci. Math. (Szeged) 80 (3-4) (2014), 511-530.

[2] Lu, Y., Liu, C., Toeplitz and Hankel products on Bergman spaces of the unit ball, Chin. Ann. Math. Ser. B 30 (3) (2009), 293-310.

[3] Lu, Y., Shang, S., Bounded Hankel products on the Bergman space of the polydisk, Canad. J. Math. 61 (1) (2009), 190-204.

[4] Miao, J., Bounded Toeplitz products on the weighted Bergman spaces of the unit ball, J. Math. Anal. Appl. 346 (1) (2008), 305-313.

[5] Michalska, M., Sobolewski, P., Bounded Toeplitz and Hankel products on the weighted Bergman spaces of the unit ball, J. Aust. Math. Soc. 99 (2) (2015), 237-249.

[6] Nazarov, F., A counter-example to Sarason’s conjecture, preprint. Available at http://www.math.msu.edu/~fedja/prepr.html.

[7] Pott, S., Strouse, E., Products of Toeplitz operators on the Bergman spaces \(A^2\), Algebra i Analiz 18 (1) (2006), 144-161 (English transl. in St. Petersburg Math. J. 18 (1) (2007), 105-118).

[8] Stroethoff, K., Zheng, D., Toeplitz and Hankel operators on Bergman spaces, Trans. Amer. Math. Soc. 329 (2) (1992), 773-794.

[9] Stroethoff, K., Zheng, D., Products of Hankel and Toeplitz operators on the Bergman space, J. Funct. Anal. 169 (1) (1999), 289-313.

[10] Stroethoff, K., Zheng, D., Invertible Toeplitz products, J. Funct. Anal. 195 (1) (2002), 48-70.

[11] Stroethoff, K., Zheng, D., Bounded Toeplitz products on the Bergman space of the polydisk, J. Math. Anal. Appl. 278 (1) (2003), 125-135.

[12] Stroethoff, K., Zheng, D., Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (1) (2007), 114-129.

[13] Stroethoff, K., Zheng, D., Bounded Toeplitz products on weighted Bergman spaces, J. Operator Theory 59 (2) (2008), 277-308.

[14] Hedenmalm, H., Korenblum, B., Zhu, K., Theory of Bergman Spaces, Springer-Verlag, New York, 2000.