正规齐型空间中的一类恒等逼近

A Class of Approximations of the Identity on Normal Space of Homogeneous Type

设δ(x,y)是正规齐型空间(x,d,μ)中的一个非对称拟距离,K_(?)是由δ(x,y)定义的一族算子,T是K_(?)的极大箅子,本文研究了T的L_p(1<p<∞曲)及弱L_1有界性,且给出了K_(?)(f)的点态恒等逼近和L_p恒等逼近。

Let δ(x,y) be a non-necessarily symmetric guasi-distance associated to a normal space of homogeneous type(X,d,μ),k8 be a class of operators associated loδ(x,y),T(f)(x) = sup s&gt;0|k (f)(x)|. In this paper, we reseached the Lp boundness and weak L1boundness of the opera-tor T, the pointwise and Lp convergent approximate identities of K8(f).