$L^p$ eigenfunction bounds for the Hermite operator

Koch, Herbert; Tataru, Daniel

Duke Math. J., Tome 126 (2005) no. 1, p. 369-392 / Harvested from Project Euclid

Résumé

We obtain $L^p$ eigenfunction bounds for the harmonic oscillator $H = -\Delta + x^2$ $H = -\Delta + x^2$ in $\mathbb{R}^n$ $\mathbb{R}^n$ and for other related operators, improving earlier results of Thangavelu and of Karadzhov. We also construct suitable counterexamples that show that our estimates are sharp.

Publié le : 2005-06-01
Classification: 35S05, 35B60

@article{1117728419,
     author = {Koch, Herbert and Tataru, Daniel},
     title = {$L^p$ eigenfunction bounds for the Hermite operator},
     journal = {Duke Math. J.},
     volume = {126},
     number = {1},
     year = {2005},
     pages = { 369-392},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1117728419}
}

Koch, Herbert; Tataru, Daniel. $L^p$ eigenfunction bounds for the Hermite operator. Duke Math. J., Tome 126 (2005) no. 1, pp.  369-392. http://gdmltest.u-ga.fr/item/1117728419/