度量测度空间上带跳扩散过程的边界哈纳克原理（BHP）
Boundary Harnack principle for diffusion with jumps on metric measure spaces
AI总结：
针对度量测度空间上与另一Hunt过程在开集退出分布估计、格林函数界及跳跃密度函数可比较性等条件下弱对偶的一大类不连续Hunt过程，本文得到了任意开集上非尺度不变的边界哈纳克原理（BHP），并通过实例说明主要结果与新贡献。
AI中文摘要：
在合适的条件下，基于开集退出分布的估计、格林函数的界以及跳跃密度函数的可比性，针对度量测度空间上与另一Hunt过程处于弱对偶关系的一大类不连续Hunt过程，本文得到了任意开集上的非尺度不变的边界哈纳克原理（BHP）。这些条件在具体情形中易于验证。本文给出了几个例子来说明主要结果和本文的新贡献。特别地，本文的结果确立了：对于度量测度空间上具有强局部项和纯跳跃项、且允许（次）高斯型与稳定型混合的双边热核估计的正则对称Dirichlet形式对应的任意Hunt过程，以及对于$\boldsymbol{\rm R}^d$上一大类非对称带跳扩散过程，其任意开集上的BHP均成立。
英文摘要：
A non-scale invariant BHP on any open set is obtained for a large class of discontinuous Hunt processes on metric measure spaces that are in weak duality with another Hunt process under suitable conditions in terms of estimates of exit distributions from open sets, and bounds on Green functions and the comparability of the jump density function. These conditions are easy to verify in concrete cases. Several examples are given to illustrate the main results and the new contributions of this paper. Our result in particular establishes the BHP on any open set for any Hunt process associated with a regular symmetric Dirichlet form on a metric measure space having both the strongly local term and the pure-jump term that admits a two-sided heat kernel estimates of the mixture of (sub-)Gaussian and stable-like form, as well as for a wide class of non-symmetric diffusion processes with jumps on $\mathbb R^d.$
