Toeplitz Operators on Dirichlet-Type Space of Unit Ball

We construct a function u in L 2 B n , d V which is unbounded on any neighborhood of each boundary point of B n such that Toeplitz operator T u is a Schatten p -class 0 < p < ∞ operator on Dirichlet-type space D B n , d V . Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space D B n , d V . 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 ξ k u is studied, where k ∈ Z n , ξ ∈ ∂ B n , and u is a radial function.