Singular Integral Operator Involving Higher Order Lipschitz Classes

In this paper, we investigate a singular integral operator with polyanalytic Cauchy kernel. In particular, we will prove that the higher order Lipschitz classes (of order 1+α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+\alpha $$\end{document}) behave invariant under the action of that operator.