Cauchy Transforms on Polynomial Curves and Related Operators
نویسندگان
چکیده
When A is a Lipschitz function, the L boundedness of %A is well understood and several proofs of it have been produced (cf. [C, CJS, CMM, DJ, M]). If A is a C -smooth function, then the local L boundedness of ̂ A is also well understood (cf. [FJR]). However, if A is a smooth, not necessarily Lipschitz function, the question of global L boundedness of ί?A has not been settled. In [KS], we observe that (6A is not, in general, bounded on L if A is a smooth non-Lipschitz function, and prove that *@ A is bounded on I if A is either a polynomial of odd degree or an even polynomial. The purpose of this paper is to give a new proof of it and to extend the result to arbitrary polynomials.
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