Abstract
In this paper we obtain a condition for analytic square integrable functions \(f,g\) which guarantees the boundedness of products of the Toeplitz operators \(T_fT_{\bar g}\) 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.
Highlights
Let D be the open unit disk in the complex plane C
In that case the Toeplitz and Hankel operators are densely defined on the Bergman space A2, that is on H∞
The main problem in this note is what conditions must be satisfied by functions f, g ∈ A2 to guarantee that the product of the Toeplitz operators Tf Tgis bounded on the Bergman space A2 in the polydisk Dn
Summary
Products of Toeplitz and Hankel operators on the Bergman space in the polydisk Abstract. In this paper we obtain a condition for analytic square integrable functions f, g which guarantees the boundedness of products of the Toeplitz operators Tf Tgdensely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators Hf Hg∗ is given
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