数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 449-463.

• 论文 •    下一篇

加倍测度空间中的热核估计

窦小曼   

  1. 清华大学数学科学系 北京 100084
  • 收稿日期:2013-05-06 修回日期:2014-04-26 出版日期:2015-06-25 发布日期:2015-06-25
  • 作者简介:窦小曼, dou.xiaoman@gmail.com
  • 基金资助:

    国家自然科学基金(11371217)资助

Obtaining Upper Bounds of Heat Kernels from Lower Bounds with Doubling Measure

Dou Xiaoman   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084
  • Received:2013-05-06 Revised:2014-04-26 Online:2015-06-25 Published:2015-06-25

摘要:

该文讨论了在加倍测度度量空间中, 热核估计的上界与下界的关系. 若相应的狄氏型满足局部性条件, 则可以由近对角下界估计推出上对角估计. 和此前这类问题的研究工作相比, 该文给出了更加一般性的结果.

关键词: 热核, 双边估计, 加倍测度

Abstract:

This paper shows the relationship between lower bounds and upper bounds of the heat kernel on metric spaces with doubling measure. If in addition the Dirichlet form is local, then a near-diagonal lower bound implies an on-diagonal upper bound. This paper gives the upper estimate in balls and then extends it to full spaces. Compared with previous work, the conclusion of this paper not only contains former result but reveals a more general relationship between the lower and upper bounds.

Key words: Heat kernels, Bounds estimates, Volume doubling measure

中图分类号: 

  • O174