A counterexample to an endpoint bilinear Strichartz inequality
| dc.creator | Tao, Terence | |
| dc.date | 2006-09-29 | |
| dc.date.accessioned | 2026-07-07T07:25:27Z | |
| dc.date.available | 2026-07-07T07:25:27Z | |
| dc.description | The endpoint Strichartz estimate $\| e^{itΔ} f \|_{L^2_t L^\infty_x(\R \times \R^2)} \lesssim \|f\|_{L^2_x(\R^2)}$ is known to be false by the work of Montgomery-Smith, despite being only ``logarithmically far'' from being true in some sense. In this short note we show that (in sharp constrast to the $L^p_{t,x}$ Strichartz estimates) the situation is not improved by passing to a bilinear setting; more precisely, if $P, P'$ are non-trivial smooth Fourier cutoff multipliers then we show that the bilinear estimate $$\| (e^{itΔ} P f) (e^{itΔ} P' g) \|_{L^2_t L^\infty_x(\R \times \R^2)} \lesssim \|f\|_{L^2_x(\R^2)} \|g\|_{L^2_x(\R^2)} $$ fails even when $P$, $P'$ have widely separated supports. | |
| dc.description | 7 pages, no figures, submitted, EJDE | |
| dc.identifier | https://arxiv.org/abs/math/0609849 | |
| dc.identifier | http://arxiv.org/abs/math/0609849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116721 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 35J10 | |
| dc.title | A counterexample to an endpoint bilinear Strichartz inequality | |
| dc.type | text |