Norms and Essential Norms of the Singular Integral Operator with Cauchy Kernel on Weighted Lebesgue Spaces

Let α and β be bounded measurable functions on the unit circle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{T}}$$\end{document}, and let L2(W) be a weighted L2 space on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{T}}$$\end{document}. The singular integral operator Sα,β is defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S_{\alpha, \beta}f = \alpha Pf + \beta Qf~ (f \in L^2(W))}$$\end{document} where P is an analytic projection and Q = I − P is a co-analytic projection. In the previous paper, the essential norm of Sα,β are calculated in the case when W is a constant function. In this paper, the essential norm of Sα,β are estimated in the case when W is an A2-weight.