AI 中文总结
研究通过上解构造证明图上一般算子哈代权重最优性的新准则，用于无杀伤项图拉普拉斯算子及分数阶拉普拉斯算子，能得到一般图和欧几里得格上的最优哈代权重。
AI 中文摘要
我们通过上解构造给出了一个新的准则，用于证明图上一般算子的哈代权重的最优性。对于无杀伤项的图拉普拉斯算子，通过格林函数总能得到最优哈代权重，无需任何进一步假设。与早期结果不同，我们的结果不限于局部有限图，这尤其使我们能够得到一般图上分数阶拉普拉斯算子的最优哈代权重。对于欧几里得格上的分数阶拉普拉斯算子，我们得到了具有预期常数和渐近性的最优哈代权重。
英文摘要
We give a new criterion to show optimality of Hardy weights for general operators on graphs via the supersolution construction. For Laplacians on graphs without killing terms this always gives rise to an optimal Hardy weight via the Green's function without any further assumptions. Furthermore, in contrast to earlier results, our result is not restricted to locally finite graphs. This allows us in particular to obtain optimal Hardy weights for the fractional Laplacian on general graphs. For the fractional Laplacian on the Euclidean lattice, we then obtain an optimal Hardy weight with the constant and asymptotics as it is expected from the continuous setting.
Comments24 pages, comments are welcome
