arXiv subjects

Kamilia Dahmani

Publications and source records attributed to Kamilia Dahmani.

2 recordsLinked to original sources

arXiv2018

Dimensionless $L^p$ estimates for the Riesz vector on manifolds

We present a new proof of the dimensionless $L^p$ boundedness of the Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion, namely that of a new dimensionless weighted $L^p$ estimate with optimal exponent. Other than previous arguments, only a small part of our proof is based on special auxiliary functions, the core of the argument is a weak type estimate and a sparse decomposition of the stochastic process by X.D. Li, whose projection is the Riesz vector.

math.PR↗

arXiv2016

Sharp dimension free bound for the Bakry-Riesz vector

We prove a sharp dimensionless weighted estimate of the Riesz vector on a Riemannian manifold with non-negative Bakry-Emery curvature. The proof is by the method of Bellman functions, where the explicit expression of a Bellman function of six variables is essential. Notice that our estimate is terms of the Poisson characteristic of the weight includes the case of the Gauss space as well as other spaces that are not necessarily of homogeneous type.

math.CA↗