Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590727 | Journal of Functional Analysis | 2013 | 20 Pages |
Abstract
By using an explicit Bellman function, we prove a bilinear embedding theorem for the Laplacian associated with a weighted Riemannian manifold (M,μφ)(M,μφ) having the Bakry–Emery curvature bounded from below. The embedding, acting on the Cartesian product of Lp(M,μφ)Lp(M,μφ) and Lq(T⁎M,μφ)Lq(T⁎M,μφ), 1/p+1/q=11/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 LpLp norms of the corresponding shifted Riesz transform. All our proofs are analytic.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrea Carbonaro, Oliver Dragičević,