A remark on bilinear pseudo-differential operators with symbols in the Sjöstrand class

Abstract

In this short note, we consider bilinear pseudo-differential operators with symbols belonging to the Sjöstrand class. We show that those operators are bounded from the product of the $L^2$-based Sobolev spaces $H^{s_1}\times H^{s_2}$ to $L^r$ for $s_1,s_2>0$, $s_1+s_2=n/2$, and $1\le r\le 2$.

11 pages. arXiv admin note: text overlap with arXiv:1908.11641, arXiv:1901.07237, arXiv:2001.04648