Toeplitz operators on Dirichlet space D~p on annulus

In this paper,the boundedness,compactness and the Fredholm properties of Toeplitz operators on the Dirichlet space Dp( M)( 1 p ∞) where M is the annulus in complex plane are discussed,and the Fredholm indices of Toeplitz operators on the Dirichlet space Dp( M) are computed. We also describe the compactness of Hankel operators on the Dirichlet space Dp( M).