# ANNALES DE L'INSTITUT FOURIER

Bilinear pseudo-differential operators with exotic symbols
Annales de l'Institut Fourier, Volume 70 (2020) no. 6, pp. 2737-2769.

The boundedness from ${L}^{p}×{L}^{q}$ to ${L}^{r}$, $1, $0<1/p+1/q=1/r\le 1$, of bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B{S}_{\rho ,\rho }^{m}$, $0\le \rho <1$, is proved for the critical order $m$. Related results for the cases $p=1$, $q=1$ or $r=\infty$ are also obtained.

On considère des opérateurs pseudo-différentiels avec des symboles dans la classe exotique de Hörmander. On prouve des estimations dans des espaces de Lebesgue pour ces opérateurs, sous l’hypothèse que leurs symboles soient dans la classe exotique de Hörmander d’ordre critique. On donne aussi des résultats reliés pour les espaces de Hardy et BMO.

Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3401
Classification: 42B15, 42B20, 47G30
Keywords: Bilinear pseudo-differential operators, bilinear Hörmander symbol classes, exotic symbols
Miyachi, Akihiko 1; Tomita, Naohito 2

1 Department of Mathematics Tokyo Woman’s Christian University Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
2 Department of Mathematics Graduate School of Science Osaka University Toyonaka, Osaka 560-0043, Japan
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Miyachi, Akihiko; Tomita, Naohito. Bilinear pseudo-differential operators with exotic symbols. Annales de l'Institut Fourier, Volume 70 (2020) no. 6, pp. 2737-2769. doi : 10.5802/aif.3401. https://aif.centre-mersenne.org/articles/10.5802/aif.3401/

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