We consider convolution operators on of the form
, where is a polynomial defined on with values in and is a smooth Calderón-Zygmund kernel on . A maximal operator can be constructed in a similar fashion. We discuss weak-type 1-1 estimates for and and the uniformity of such estimates with respect to . We also obtain -estimates for "supermaximal" operators, defined by taking suprema over ranging in certain classes of polynomials of bounded degree.
Cite this article
Anthony Carbery, Fulvio Ricci, James Wright, Maximal functions and singular integrals associated to polynomial mappings of . Rev. Mat. Iberoam. 19 (2003), no. 1, pp. 1–22DOI 10.4171/RMI/336