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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

## Author

### Hong-Quan Li

### Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

### Yurong Wu

#### Mathematische Zeitschrift

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

Vol. 282 3 623-633### Roots

Basic sciences

### Subject Categories

Mathematical Analysis

### DOI

10.1007/s00209-015-1555-z