具有反对称核、相关容量和Wolff势的奇异算子
Singular operators with antisymmetric kernels, related capacities, and Wolff potentials
摘要：
我们考虑推广的Riesz算子在$R^d$和获得估计其范数和相关的能力，通过修改的沃尔夫潜力。这些估计是基于度量空间中Calderón-Zygmund算子的$T1$定理的某个版本。本文将$R^d$中的两种Calderón-Zygmund容量推广到度量空间，并在一定条件下建立了它们的等价性.作为应用，我们将已知的$s$ -Riesz容量$0<s<d$与非线性位势论中的容量之间的关系推广到$s=0$的情形.
英文摘要：
We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for Calderón-Zygmund operators in metric spaces. We extend two versions of Calderón-Zygmund capacities in $R^d$ to metric spaces and establish their equivalence (under certain conditions). As an application, we extend the known relations between $s$-Riesz capacities, $0<s<d$, and the capacities in Nonlinear Potential Theory, to the case $s=0$.
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