Preprint, 2017

Let $v \ne 0$ be a vector in $\R^n$.
Consider the Laplacian on $\R^n$ with drift
$\Delta_{v} = \Delta + 2v\cdot \nabla$ and the measure $d\mu(x) = e^{2 \langle v, x \rangle}
dx$, with respect to which $\Delta_{v}$ is self-adjoint.
%Let $d$ and $\nabla$ denote the Euclidean distance and the gradient operator on $\R^n$. Consider the space $(\R^n, d,d\mu)$, which has the property of exponential volume growth.
This measure has exponential growth with respect to the Euclidean distance.
We study weak type $(1, 1)$ and other sharp endpoint estimates for the Riesz
transforms of any order, and also for the vertical and horizontal
Littlewood-Paley-Stein
functions associated with the heat and the Poisson semigroups.

Laplacian with drift

Littlewood-Paley-Stein operators

Riesz transform

Heat semigroup

University of Gothenburg

Chalmers, Mathematical Sciences

Mathematics

Basic sciences