$L\sp p$-$L\sp q$ regularity of Fourier integral operators with caustics
| dc.creator | Comech, Andrew | |
| dc.date | 2006-09-01 | |
| dc.date.accessioned | 2026-07-07T07:24:24Z | |
| dc.date.available | 2026-07-07T07:24:24Z | |
| dc.description | The caustics of Fourier integral operators are defined as caustics of the corresponding Schwartz kernels (Lagrangian distributions on $X\times Y$). The caustic set $Σ(C)$ of the canonical relation $C$ is characterized as the set of points where the rank of the projection $π:C\to X\times Y$ is smaller than its maximal value, $dim(X\times Y)-1$. We derive the $L\sp p(Y)\to L\sp q(X)$ estimates on Fourier integral operators with caustics of corank 1 (such as caustics of type $A\sb{m+1}$, $m\in\N$). For the values of $p$ and $q$ outside of certain neighborhood of the line of duality, $q=p'$, the $L\sp p\to L\sp q$ estimates are proved to be caustics-insensitive. We apply our results to the analysis of the blow-up of the estimates on the half-wave operator just before the geodesic flow forms caustics. | |
| dc.description | 24 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0609024 | |
| dc.identifier | http://arxiv.org/abs/math/0609024 | |
| dc.identifier | Trans. Amer. Math. Soc. 356 (2004), no. 9, 3429--3454 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116338 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35S30 | |
| dc.title | $L\sp p$-$L\sp q$ regularity of Fourier integral operators with caustics | |
| dc.type | text |