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

Hong-Quan Li ; Peter Sjögren (Institutionen för matematiska vetenskaper, matematik) ; Yurong Wu
Mathematische Zeitschrift (0025-5874). Vol. 282 (2016), 3, p. 623-633.

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

CPL Pubid: 202555

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Institutionen för matematiska vetenskaper, matematik (2005-2016)