Bilinear pseudo-differential operators with exotic symbols

Miyachi, Akihiko; Tomita, Naohito

doi:10.5802/aif.3401

Bilinear pseudo-differential operators with exotic symbols
[Opérateurs pseudo-différentiels bilinéaires avec symboles exotiques]

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

Annales de l'Institut Fourier, Tome 70 (2020) no. 6, pp. 2737-2769.

Résumé
Abstract

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.

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

Reçu le : 2017-05-19
Révisé le : 2017-09-17
Accepté le : 2017-11-07
Publié le : 2021-04-15

DOI : 10.5802/aif.3401

Classification : 42B15, 42B20, 47G30
Keywords: Bilinear pseudo-differential operators, bilinear Hörmander symbol classes, exotic symbols
Mot clés : opérateurs pseudo-différentiels bilinéaires, symbole exotique

Affiliations des auteurs :

Miyachi, Akihiko ¹ ; Tomita, Naohito ²

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Miyachi, Akihiko; Tomita, Naohito. Bilinear pseudo-differential operators with exotic symbols. Annales de l'Institut Fourier, Tome 70 (2020) no. 6, pp. 2737-2769. doi : 10.5802/aif.3401. http://archive.numdam.org/articles/10.5802/aif.3401/

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