标题： 非局部方程一类的梯度正则性和一阶势估计 显示英文标题

标题： Gradient regularity and first-order potential estimates for a class of nonlocal equations

摘要： 我们考虑具有测度数据的高阶非局部方程，并证明在Sobolev和Hölder空间中的梯度正则性，以及梯度的点态界，这些界用Riesz势表示，从而在许多常用函数空间中得到精细的正则性结果。 积分算子的核在变量中具有Hölder依赖性，并且不假设为平移不变。 显示英文摘要

摘要： We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity results in many commonly used function spaces. The kernel of the integral operators involves a H\"older dependence in the variables and is not assumed to be translation invariant.