Hankel and slant Hankel operators on the Bergman space of the polydisk

Abstract

In this paper, for n ≥ 1, we initiate the notion of Hankel operators on the polydisk Dⁿ and slant Hankel operators on L²(Tⁿ) where Tⁿ denotes the n-torus. We give the necessary and sufficient condition for a bounded operator on L²(Tⁿ) to be a slant Hankel operator and study some algebraic properties of slant Hankel operators. Also, we extend our study on the Bergman space.