Singular integral operators associated to curves with rational components

Abstract

We prove L-p(R-n),1 &lt; p &lt; infinity, bounds for[GRAPHICS]and[GRAPHICS]where R-j(t) = P-j(t)/Q(j)(t),j = 1,2...,n, are rational functions. Our bounds depend only on the degrees of the polynomials P-j, Q(j) and, in particular, they do not depend on the coefficients of these polynomials.</p