The $\square_b$ Heat Equation and Multipliers via the Wave Equation
| dc.creator | Street, Brian | |
| dc.date | 2008-05-09 | |
| dc.date | 2008-09-10 | |
| dc.date.accessioned | 2026-07-07T10:01:35Z | |
| dc.date.available | 2026-07-07T10:01:35Z | |
| dc.description | Recently, Nagel and Stein studied the $\square_b$-heat equation, where $\square_b$ is the Kohn Laplacian on the boundary of a weakly-pseudoconvex domain of finite type in $\C^2$. They showed that the Schwartz kernel of $e^{-t\square_b}$ satisfies good "off-diagonal" estimates, while that of $e^{-t\square_b}-π$ satisfies good "on-diagonal" estimates, where $π$ is the Szegö projection. We offer a simple proof of these results, which easily generalizes to other, similar situations. Our methods involve adapting the well-known relationship between the heat equation and the finite propagation speed of the wave equation to this situation. In addition, we apply these methods to study multipliers of the form $mł(\square_b\r)$. In particular, we show that $mł(\square_b\r)$ is an NIS operator, where $m$ satisfies an appropriate Mihlin-Hörmander condition. | |
| dc.description | 29 pages; minor corrections | |
| dc.identifier | https://arxiv.org/abs/0805.1291 | |
| dc.identifier | http://arxiv.org/abs/0805.1291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168676 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 32W30; 32T25; 32V35; 32W10 | |
| dc.title | The $\square_b$ Heat Equation and Multipliers via the Wave Equation | |
| dc.type | text |