Bilinear pseudo-differential operators with exotic symbols

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 Hörmander class $B{S}_{\rho ,\rho }^m$, $0\le \rho <1$, is proved for the critical order $m$. Related results for the cases $p=1$, $q=1$ or $r=\infty$ are also obtained.

24 pages. To appear in Ann. Inst. Fourier (Grenoble)

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