Maximal functions and singular integrals associated to polynomial mappings of IR<i><SUP>n</SUP></i>

作     者：Carbery, A Ricci, F Wright, J 

作者机构：Univ Edinburgh Dept Math & Stat Edinburgh EH9 3JZ Midlothian Scotland Scuola Normale Super Pisa Dipartimento Matemat I-56126 Pisa Italy 

出 版 物：《REVISTA MATEMATICA IBEROAMERICANA》 (Rev. Mat. Iberoam.)

年 卷 期：2003年第19卷第1期

页      面：1-22页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：maximal functions singular integrals weak-type estimates 

摘      要：We consider convolution operators on R-n of the form T(P)f(x) = integral(Rm) f(x - P(y))K(y)dy, where P is a polynomial defined on R-m with values in R-n and K is a smooth Calderon-Zygmund kernel on 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 supermaximar operators, defined by taking suprema over P ranging in certain classes of polynomials of bounded degree.