Bilinear pseudo-differential operators with exotic class symbols of limited smoothness

Abstract

We consider bilinear pseudo-differential operators with symbols in the bilinear Hörmander class, $B{S}_{\rho ,\rho }^m$, $m\in \mathbb{R}$, $0\le \rho <1$. The aim of this paper is to discuss low regularity conditions for symbols to assure the boundedness from $L^2\times L^2$ to $h^1$ and from $L^2\times bmo$ to $L^2$.

40 pages

Cited by in corpus (2)

• On the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2\times L^2$
• Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0,0}$-type in the scale of Besov spaces