Weighted Poincaré Inequalities for Non-local Dirichlet Forms
Weighted Poincaré Inequalities for Non-local Dirichlet Forms
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DOI：
10.1007/s10959-015-0650-8
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发表时间：
2015-10
影响因子：
0.8
通讯作者：
Xin Chen;Jian Wang
中科院分区：
文献类型：
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作者：
Xin Chen;Jian Wang
令 V 为局部有界可测函数，即概率测度。给出了以下非局部狄利克雷形式的加权庞加莱不等式的显式标准 $$\begin{aligned} \hat{D}_{\rho ,V}(f,f)=\iint _{\{|x-y|>1\}}(f(y)-f(x))^2\rho (|y-x|)\,\mathrm{d}y\, \mu _V(\mathrm{d}x)。 \end{aligned}$$Takingwithand，我们得到了（指数）调和分数狄利克雷形式的新结论，这不仅完成了我们最近的工作（Chen 和 Wang 发表在 Stoch Process Their Appl 124:123–153, 2014；Wang 和 Wang 发表在 J Theor Probab 28:423–448, 2015），而且还改进了 Mouhot 等人的主要结果。 (J Math Pures Appl 95:72–84, 2011)。
LetVbe a locally bounded measurable function onsuch thatis a probability measure. Explicit criteria are presented for weighted Poincaré inequalities of the following non-local Dirichlet form $$\begin{aligned} \hat{D}_{\rho ,V}(f,f)=\iint _{\{|x-y|>1\}}(f(y)-f(x))^2\rho (|y-x|)\,\mathrm{d}y\, \mu _V(\mathrm{d}x). \end{aligned}$$Takingwithand, we get new conclusions for (exponentially) tempered fractional Dirichlet forms, which not only complete our recent work (Chen and Wang in Stoch Process Their Appl 124:123–153, 2014; Wang and Wang in J Theor Probab 28:423–448, 2015), but also improve the main result in Mouhot et al. (J Math Pures Appl 95:72–84, 2011).