Singular integral operators associated to curves with rational components

We prove $L^p ({\mathbb{R}}^n), 1<p<\infty$, bounds for

$Hf(x) = p.v. \int_{-\infty}^{\infty} f(x_1 - R_1 (t), \ldots , x_n - R_n (t) ) \, dt/t$

and

$Mf(x) = \sup_{h>0} {1\over h} \int_{0}^{h} \vert f(x_1 - R_1 (t), \ldots , x_n - R_n (t) )\vert \, dt$

where $R_j (t) = P_j(t)/Q_j(t), j=1,2,\ldots, n$, 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.