Global heat kernel estimate for relativistic stable processes in exterior open sets

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• 作者：Zhen-Qing Chen^a ; ¹ ; ^{zqchen@uw.edu} ; Panki Kim^b ; ² ; ^{pkim@snu.ac.kr} ; Renming Song^c ; ³ ; ^{rsong@math.uiuc.edu}
• 关键词：Symmetric 伪-stable process ; Relativistic stable process ; Heat kernel ; Transition density ; Green function ; Exit time ; L&eacute ; vy system ; Parabolic Harnack inequality
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 July, 2012
• 卷：263
• 期：2
• 页码：448-475
• 文件大小：239 K

摘要

In this paper, sharp two-sided estimates for the transition densities of relativistic 伪-stable processes with mass in exterior open sets are established for all time . These transition densities are also the Dirichlet heat kernels of with in exterior open sets. The estimates are uniform in m in the sense that the constants are independent of . As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic 伪-stable processes with mass in exterior open sets.