Weak type (1,1) of some operators for the Laplacian with drift

Journal article, 2016

Let $\Delta_{v} = \Delta + 2v\cdot \nabla $ be the Laplacian with drift in $\R^n$. Here $v$ is any nonzero vector. Then $\Delta_{v}$ has a self-adjoint extension in $L^2(\mu)$ for the measure $d\mu(x) = e^{2 \langle v, x \rangle}dx$. Clearly, this measure has exponential volume growth with respect to the Euclidean metric. We prove the weak type (1,1) boundedness of the corresponding Riesz transforms and the heat maximal operator, with respect to $\mu$. These operators were already known to be bounded on $L^p(\mu),\;1