AI 中文总结
该研究在加倍度量测度空间上，针对带非标准(p,q)-Orlicz增长的非局部算子，证明了齐次非局部方程弱解的局部Hölder正则性，相关结果在欧氏情形下也属首次。
AI 中文摘要
在加倍度量测度空间上，我们研究具有非标准(p,q)-Orlicz增长（1<p≤q<∞）的非局部算子，其中相互作用核由一般的非平移不变测度给出。在相互作用测度满足对称性、合适的非局部庞加莱不等式和尾界的自然假设下，我们证明对应齐次非局部方程的每个弱解都存在局部Hölder连续的代表元。即使在欧氏情形下，这些正则性结果也是新的。
英文摘要
On doubling metric measure spaces, we study nonlocal operators with non-standard $(p,q)$-Orlicz growth ($1<p\leq q<\infty$), where the interaction kernel is given by a general, non-translation-invariant measure. Under natural assumptions on the interaction measure - namely symmetry, a suitable nonlocal Poincaré inequality, and a tail bound - we prove that every weak solution to the corresponding homogeneous nonlocal equation admits a locally Hölder continuous representative. These regularity results are new even in the Euclidean setting.
