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

摘要

Let α and β be bounded measurable functions on the unit circle , and let L 2(W) be a weighted L 2 space on . The singular integral operator S _α,β is defined by where P is an analytic projection and Q = I − P is a co-analytic projection. In the previous paper, the essential norm of S _α,β are calculated in the case when W is a constant function. In this paper, the essential norm of S _α,β are estimated in the case when W is an A ₂-weight.