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arXiv · 1801.06744

Bilinear pseudo-differential operators with exotic symbols

Akihiko Miyachi·Naohito Tomita
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Abstract

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

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Akihiko Miyachi, Naohito Tomita. 2018-01-21. Bilinear pseudo-differential operators with exotic symbols. https://arxiv.org/abs/1801.06744

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