Abstract
We consider the bilinear pseudo-differential operators with symbols in the bilinear Hörmander classes $BS_{\rho, \rho}^m$, $0 \lt \rho \lt 1$. In this paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary to assure the boundedness from $H^{p_1} \times H^{p_2}$ to $L^p$ of those operators with the critical order $m$.
Funding Statement
This work was partially supported by JSPS KAKENHI Grant Numbers JP20K14339 (Kato).
Acknowledgment
The authors sincerely express their thanks to Professor Akihiko Miyachi and Professor Naohito Tomita for valuable discussions and fruitful advices. The authors also express thanks to the anonymous referees for their careful reading and helpful suggestions.
Citation
Tomoya KATO. Naoto SHIDA. "A remark on the condition $1/p = 1/p_1 + 1/p_2$ for boundedness of bilinear pseudo-differential operators with exotic symbols." Hokkaido Math. J. 52 (2) 285 - 300, June 2023. https://doi.org/10.14492/hokmj/2021-539
Information
