Bounded Toeplitz products on Bergman spaces of the unit ball

Abstract

We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products T f Tḡ are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

Products of Toeplitz Operators on a Vector Valued Bergman Space

“…The results generalize those in the scalar valued Bergman space case [4]. We also characterize boundedness and invertibility of Toeplitz products T F T G * in terms of the Berezin transform, generalizing results found by Zheng and Stroethoff for the scalar valued Bergman space [8]. …”

“…The proof of the following theorem follows the lines of of Theorem 2.1 in [6] and Theorem 4.1 in [8]. It contains the key to the proof of Theorem 1.4 i.e.…”

Bounded Toeplitz Products on the Bergman Space of the Unit Ball in $$\mathbb{C}^n $$

“…Recently Stroethoff and Zheng[11] proved the same results in different methods. They constructed the inner product formula which is different from (1.2).…”

Toeplitz and Hankel products on Bergman spaces of the unit ball

“…Stroethoff and Zheng showed the analogous result on the Bergman space of the polydisk in [8] and on the weighted Bergman space of the unit disk in [9] and the unit ball in [10]. In [11], Park gave the analogous result for Toeplitz products on the Bergman space of the unit ball.…”

“…The following inner product formula in A 2 α will play an important role in this paper, which was proved in [10].…”