Singular integral operators with non-smooth kernels on irregular domains
Singular integral operators with non-smooth kernels on irregular domains
复制标题
DOI：
10.4171/rmi/255
复制
发表时间：
1999-08
影响因子：
1.2
通讯作者：
X. Duong;A. Mcintosh
中科院分区：
文献类型：
--
作者：
X. Duong;A. Mcintosh
设?为一个齐型空间。本文目的如下。
i) 假设\(T\)是\(L^2(?)\)上的有界线性算子，我们对\(T\)的核给出一个充分条件，使得\(T\)是弱\((1,1)\)型的，从而对\(1<p<\infty\)在\(L^p(?)\)上有界。
ii) 我们考虑极大算子\(T^*\)，其定义为\(T^*u(x)=\sup_{0<r<\infty}|T_{r}u(x)|\)，其中\(T_{r}\)是与\(T\)相关的某个算子，并给出\(T^*\)为\(L^p\)有界（\(1<p<\infty\)）的充分条件。应用包括某些里斯变换的弱\((1,1)\)估计，以及不规则区域上线性椭圆算子的全纯函数演算的\(L^p\)有界性。
Let ? be a space of homogeneous type. The aims of this paper are as follows. i) Assuming that T is a bounded linear operator on L2(?), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(?) for 1 0 |Teu(x)|, to be Lp bounded, 1 < p < 8. Applications include weak (1,1) estimates of certain Riesz transforms, and Lp boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains.