Toeplitz operators on Hardy-Sobolev spaces

In this paper, we construct compact Toeplitz operators and trace class Toeplitz operators with unbounded symbols on Hardy-Sobolev spaces. We also characterize the compactness of finite sums of products of two Toeplitz operators on these spaces. Then, we study the Fredholmness of the Toeplitz operators and calculate the essential norm of them. In addition, we consider the C ⁎ -algebra generated by Toeplitz operators.