On quasinormality of singular integral operators with Cauchy kernel on $L^{2}$

Abstract

We study the quasinormality of singular integral operators with Cauchy kernel on $L^2$. Moreover, we give characterizations for singular integral operators to be the square root of a self-adjoint operator and an isometry, respectively. Furthermore, we consider the condition for singular integral operators to be $D$-operators. We provide several results and examples of such operators as applications.