Toeplitz Operators on Dirichlet-Type Space of Unit Ball

We construct a function u in L-2 (B-n, dv) 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 < infinity) operator on Dirichlet-type space D(B-n, dv). Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space D(B-n, dv). 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 xi(k) u is studied, where k epsilon partial derivative B-n, and u is a radial function.