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

Författare

Hong-Quan Li

Peter Sjögren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Yurong Wu

Mathematische Zeitschrift

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

Vol. 282 3 623-633

Fundament

Grundläggande vetenskaper

Ämneskategorier

Matematisk analys

DOI

10.1007/s00209-015-1555-z

Mer information

Skapat

2017-10-07