摘要
本文考虑齐型空间上的恒等逼近算子。文中去掉Aimar的文章中关于齐型空间是α阶的及满足性质P的假定,同时保留其关于核的条件,重新证明了算子族K_e(f)的极大算子T是弱(1,1)型及(P,P)型的,P>1。还进一步研究了K_e(f)的点收敛,L^P收敛及非切向收敛的推广。
In this paper we consider a class of approximations of the identity. Removing the hypothesis in Aimar's paper that the space of homogeneous type (X, d, μ)is a space of order α satisfying property P, and keeping his condition on the family of kernels, we use another method to prove that the maximal operator T of the family of operators K,(f) is of weak type (1,1) and strong type (p,p), p>1. Furthermore, we study the problems of pointwise convergence, Lp-convergence and generalized non-tangential convergence of K.(f)
出处
《北京大学学报（自然科学版）》
CAS
CSCD
北大核心
1992年第5期513-521,共9页
Acta Scientiarum Naturalium Universitatis Pekinensis
基金
国家自然科学基金
关键词
齐型空间
恒等逼近
卷积算子
Spaces of homogeneous type
Approximations of the identity
