Maximal functions and singular integrals associated to polynomial mappings of $\mathbb{R}^n$

We consider convolution operators on \mathbb{R}^n of the form T_Pf(x) =\int_{\mathbb{R}^m} f\big(x-P(y)\big)K(y) dy , where P is a polynomial defined on \mathbb{R}^m with values in \mathbb{R}^n and K is a smooth Calderón-Zygmund kernel on \mathbb{R}^m . A maximal operator M_P can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for T_P and M_P and the uniformity of such estimates with respect to P . We also obtain L^p -estimates for "supermaximal" operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.