Bellman function and linear dimension-free estimates in a theorem of D. Bakry

Details Bellman function and linear dimension-free estimates in a theorem of D. Bakry Bellman function and linear dimension-free estimates in a theorem of D. Bakry

2011-05-31

arxiv.org/abs/1105.6330v1

Mathematics

Functional Analysis

12 pages

Scientific paper

By using an explicit Bellman function, we prove a bilinear embedding theorem for the Laplacian associated with a weighted Riemannian manifold $(M,\mu_\phi)$ having the Bakry-Emery curvature bounded from below. The embedding, acting on the cartesian product of $L^p(M,\mu_\phi)$ and $L^q(T^*M,\mu_\phi)$, $1/p+1/q=1$, involves estimates which are independent of the dimension of the manifold and linear in $p$. As a consequence we obtain linear dimension-free estimates of the $L^p$ norms of the corresponding shifted Riesz transform. All our proofs are analytic.

Affiliated with

Also associated with

No associations

Rating

Bellman function and linear dimension-free estimates in a theorem of D. Bakry 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 Bellman function and linear dimension-free estimates in a theorem of D. Bakry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bellman function and linear dimension-free estimates in a theorem of D. Bakry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-338931