Product and Commutativity of k th-Order Slant Toeplitz Operators

Abstract

The commutativity of $k$th-order slant Toeplitz operators with harmonic polynomial symbols, analytic symbols, and coanalytic symbols is discussed. We show that, on the Lebesgue space and Bergman space, necessary and sufficient conditions for the commutativity of $k$th-order slant Toeplitz operators are that their symbol functions are linearly dependent. Also, we study the product of two $k$th-order slant Toeplitz operators and give some necessary and sufficient conditions.