Title: Stability of Hölder regularity and weighted functional inequalities Show Chinese title

Title: Hölder正则性与加权泛函不等式的稳定性

Abstract: We study symmetric Dirichlet forms on metric measure spaces, which may possess both strongly local and pure-jump parts. We introduce a new formulation of a tail condition for jump measures and weighted functional inequalities. Our framework accommodates Dirichlet forms with singular jump measures and those associated with trace processes of mixed-type stable processes. Using these new weighted functional inequalities, we establish stable, equivalent characterizations of H\"older regularity for caloric and harmonic functions. As an application of our main result, we prove the H\"older continuity of caloric functions for a large class of symmetric Markov processes exhibiting boundary blow-up behavior, among other results. Show Chinese abstract

Abstract: 我们研究了度量测度空间上的对称狄利克雷型，这些空间可能同时具有强局部部分和纯跳跃部分。 我们引入了跳跃测度和加权泛函不等式的一种新的尾部条件公式。 我们的框架涵盖了奇异跳跃测度的狄利克雷型以及与混合型稳定过程迹过程相关的狄利克雷型。 利用这些新的加权泛函不等式，我们建立了关于热函数和调和函数的 Hölder 正则性的稳定且等价的刻画。 作为主要结果的应用，我们证明了一大类表现出边界爆发现象的对称马氏过程的热函数的 Hölder 连续性，以及其他结果。