Sharp Function Estimates for Bilinear Pseudo-Differential Operators

Let $0 lt;\varrho lt;1$ and $T_{a}$ be a bilinear pseudo-differential operator defined by the symbol $a\in BS^{-n(1-\varrho)}_{\varrho,\varrho}$. It is shown that the operator $T_{a}$ obeys the following pointwise estimate for all $x\in\mathbb{R}^{n}$ if $2 lt; p,q lt;\infty$ and $\frac{1}{p}+\frac{1}{q}=\frac{1}{2}$. Here $M^{\sharp}$ denotes the Fefferman-Stein sharp operator and $M_{p}$ stands for the generalized Hardy-Littlewood maximal operator.