We construct a function in which is unbounded on any neighborhood of each boundary point of such that Toeplitz operator is a Schatten -class operator on Dirichlet-type space . Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space . We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the form is studied, where , , and is a radial function.
Jin Xia. Xiaofeng Wang. Guangfu Cao. "Toeplitz Operators on Dirichlet-Type Space of Unit Ball." Abstr. Appl. Anal. 2014 1 - 13, 2014. https://doi.org/10.1155/2014/927513