In this article, we consider a class of integral operators on the Bergman space over the upper half-plane. We characterize the integral kernels so that the operators are bounded. We show that the collection of all such bounded integral operators coincide with the well-known class of angular operators. In other words, we provide integral representation for the class of angular operators. In terms of the integral representation, we study various operator theoretic properties of angular operators. Also, we give integral representation for all operators in the C*-algebra generated by Toeplitz operators with angular defining symbols.

The first author thanks the University Grant Commission (UGC), India for providing financial support. The authors thank the editor for helpful suggestions and pointing out missing references. The authors also thank the referee(s) for meticulously reading our manuscript and giving us several valuable suggestions which improved the clarity of the paper.