标题： 关于Choquet积分和点估计 显示英文标题

标题： On Choquet integrals and pointwise estimates

摘要： 我们考虑在Choquet意义下定义的积分不等式，相对于Hausdorff内容。 我们研究连续可微函数在开连通集上定义的情况，这些函数具有足够的正则性，使得在集合的每个点上，函数值与其梯度之间存在逐点估计，该估计在极大算子或Riesz位势下成立。 我们证明某些Hardy不等式和Poincare-Sobolev不等式在此背景下是有效的。 显示英文摘要

摘要： We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defined on open, connected sets with so much regularity that there exists a pointwise estimate between the values of a function and its gradient under the maximal operator or the Riesz potential, at every point of the set. We show that certain Hardy inequalities and Poincare-Sobolev inequalities are valid in this context.