Weak type (1,1) of some operators for the Laplacian with drift
Artikel i vetenskaplig tidskrift, 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


Hong-Quan Li

Peter Sjögren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Yurong Wu

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 282 623-633


Grundläggande vetenskaper


Matematisk analys