A counterexample to a multilinear endpoint question of Christ and Kiselev
| dc.creator | Muscalu, Camil | |
| dc.creator | Tao, Terence | |
| dc.creator | Thiele, Christoph | |
| dc.date | 2001-08-23 | |
| dc.date | 2002-02-14 | |
| dc.date.accessioned | 2026-07-07T04:43:05Z | |
| dc.date.available | 2026-07-07T04:43:05Z | |
| dc.description | Christ and Kiselev have established that the generalized eigenfunctions of one-dimensional Dirac operators with $L^p$ potential $F$ are bounded for almost all energies for $p < 2$. Roughly speaking, the proof involved writing these eigenfunctions as a multilinear series $\sum_n T_n(F, ..., F)$ and carefully bounding each term $T_n(F, ..., F)$. It is conjectured that the results of Christ and Kiselev also hold for $L^2$ potentials $F$. However in this note we show that the bilinear term $T_2(F,F)$ and the trilinear term $T_3(F,F,F)$ are badly behaved on $L^2$, which seems to indicate that multilinear expansions are not the right tool for tackling this endpoint case. | |
| dc.description | 9 pages, no figures, to appear, Math. Res. Letters. More detailed remarks, many minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0108156 | |
| dc.identifier | http://arxiv.org/abs/math/0108156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62065 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 42B15; 42B25, 35P20 | |
| dc.title | A counterexample to a multilinear endpoint question of Christ and Kiselev | |
| dc.type | text |