Fredholm and Schatten Class Operators on Bergman Spaces with Exponential Weights

In this paper, we give a characterization of Fredholmness of the Toeplitz operators on the Bergman spaces $A_{\phi }^p$ with exponential weights in $\mathbb{D}$ when $0<p<\infty$ . Also, we obtain the sufficient and necessary conditions which the Toeplitz and Hankel operators on $A_{\phi }^2$ belong to $h$ -Schatten class, where $h$ is a continuous increasing convex function.