Bilinear pseudo-differential operators with exotic symbols, II

The boundedness from $H^p\times L^2$ to $L^r$, $1\mathrm{/}p+1\mathrm{/}2=1\mathrm{/}r$, 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 H"ormander 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 $L^r$, $1\mathrm{/}p+1\mathrm{/}q=1\mathrm{/}r$, of those operators in the full range $0<p,q\le \mathrm{\infty }$, where $L^r$ is replaced by $BMO$ if $r=\mathrm{\infty }$.