A remark on the relationship $1/p=1/p_1+1/p_2$ for boundedness of bilinear pseudo-differential operators with exotic symbols

Abstract

We consider the bilinear pseudo-differential operators with symbols in the bilinear Hörmander classes $B{S}_{\rho ,\rho }^m$, $0<\rho <1$. In this paper, we show that the condition $1/p=1/p_1+1/p_2$ is necessary when we consider the boudnedness from $H^{p_1}\times H^{p_2}$ to $L^p$ of those operators for the critical case.

10 pages, 2 figures