Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

Details Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

2010-10-23

arxiv.org/abs/1010.4904v2

Mathematics

Probability

23 pages

Scientific paper

In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\alpha$-harmonic extension of an $L^p(\mathbb{R}^d)$ function.

Affiliated with

Also associated with

No associations

Rating

Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-116034