Krikeles, Basil C. Weighted \(L^ p\) estimates for the Cauchy integral operator. (English) Zbl 0552.42008 Mich. Math. J. 30, 231-244 (1983). 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. Reviewer: Z.He Cited in 1 Review MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) Keywords:Cauchy integral operator for a curve; weighted \(L^ p\) estimates; weak- type (1,1) estimate PDFBibTeX XMLCite \textit{B. C. Krikeles}, Mich. Math. J. 30, 231--244 (1983; Zbl 0552.42008) Full Text: DOI