Two-sided estimates of heat kernels on metric measure spaces
نویسندگان
چکیده
3 Some preparatory results 18 3.1 Green operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Harmonic functions and Harnack inequality . . . . . . . . . . . . . . . 22 3.3 Faber-Krahn inequality and mean exit time . . . . . . . . . . . . . . . 24 3.4 Estimates of the exit time . . . . . . . . . . . . . . . . . . . . . . . . . 27 ∗Partially supported by SFB 701 of the German Research Council †Partially supported by a visiting grant of SFB 701 of the German Research Council
منابع مشابه
Stability of heat kernel estimates for symmetric jump processes on metric measure spaces
In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, modifications of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particu...
متن کاملOn Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
متن کاملComparison inequalities for heat semigroups and heat kernels on metric measure spaces
We prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form. As a consequence of this inequality, we obtain various interesting comparison inequalities for heat semigroups and heat kernels, which can be used for obtaining pointwise estimates of heat kernels. As an example of application, we present a new method of deducing sub-Gaussian upper bou...
متن کاملNotes on Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality. AMS 2000 Mathematics Subject Classification: Primary 60J75 , 60J35, Secondary 31C25 , 31C05. Running title: Notes on Heat Kernel Estimates and Parabolic Harnack Inequality
متن کاملLaws of the Iterated Logarithm for Symmetric Jump Processes
Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010