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

Let ?? and ?? be bounded measurable functions on the unit circle ${mathbb{T}}$ , and let L ²(W) be a weighted L ² space on ${mathbb{T}}$ . The singular integral operator S _??,?? is defined by ${S_{alpha, beta}f = alpha Pf + beta Qf~ (f in L^2(W))}$ where P is an analytic projection and Q = I ? P is a co-analytic projection. In the previous paper, the essential norm of S _??,?? are calculated in the case when W is a constant function. In this paper, the essential norm of S _??,?? are estimated in the case when W is an A ₂-weight.