Weighted \(L^ p\) estimates for the Cauchy integral operator (Q801503)

The author discusses the Cauchy integral operator for a curve, which was studied by Calderon, Coifman, Meyer, McIntosh and David. He gives a direct derivation of weighted \(L^ p\) estimates for the operator with weights that can be explicitly exhibited in a way that clarifies the role played by geometry of the curve. A weak-type (1,1) estimate is also given in this paper. The proof of the results is interesting, it provides a good illustration of the interplay between analysis and geometry.