论文标题
最大奇异积分运算符作用于非交通$ l_p $ - 空格
Maximal singular integral operators acting on noncommutative $L_p$-spaces
论文作者
论文摘要
在本文中，我们研究了作用于非交通性$ l_p $ - 空格的最大Calderón-Zygmund运算符的界限理论。我们的第一个结果是针对非交通性最大Calderón-Zygmund运营商的弱类型$（1,1）$估计的标准；作为应用程序，我们获得了在适当的{juromantity}条件下的运算符值最大近距离积分的弱类型$（1,1）$估计。这些是线性运算符家族的{\ it首先}非交通性最大不平等，无法将其简化为积极。对于均匀的奇异积分，强型$（P，P）$（$ 1 <P <\ infty $）最大估计被证明是正确的，即使对于{Rough}内核也是如此。 作为标准的副产品，我们获得了具有正规度不平衡条件的Calderón-Zygmund运算符的非交通性弱型$（1,1）$估计值，比Hörmander条件稍强。这证明了在非交流性calderón-zygmund理论中对一个公开问题的肯定答案。
In this paper, we study the boundedness theory for maximal Calderón-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calderón-Zygmund operators; as an application, we obtain the weak type $(1,1)$ estimates of operator-valued maximal singular integrals of convolution type under proper {regularity} conditions. These are the {\it first} noncommutative maximal inequalities for families of linear operators that can not be reduced to positive ones. For homogeneous singular integrals, the strong type $(p,p)$ ($1<p<\infty$) maximal estimates are shown to be true even for {rough} kernels. As a byproduct of the criterion, we obtain the noncommutative weak type $(1,1)$ estimate for Calderón-Zygmund operators with integral regularity condition that is slightly stronger than the Hörmander condition; this evidences somewhat an affirmative answer to an open question in the noncommutative Calderón-Zygmund theory.
