Bilinear pseudo-differential operators with exotic symbols, II

Abstract

The boundedness from $H^p\times L^2$ to $L^r$, $1/p+1/2=1/r$, and from $H^p\times L^{\infty }$ to $L^p$ of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear Hörmander class $B{S}_{\rho ,\rho }^m$, $0\le \rho <1$, of critical order $m$, where $H^p$ is the Hardy space. This combined with the previous results of the same authors establishes the sharp boundedness from $H^p\times H^q$ to $L^r$, $1/p+1/q=1/r$, of those operators in the full range $0<p,q\le \infty$, where $L^r$ is replaced by $BMO$ if $r=\infty$.

arXiv comment13 pages