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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.