Sharp Function Estimates for Bilinear Pseudo-Differential Operators

Let 0 < rho < 1 and T-a be a bilinear pseudo-differential operator defined by the symbol a epsilon BS rho,rho-n(1- rho) .It is shown that the operator T-a obeys the following pointwise estimate M (#) (Ta( f, g))(x) <= CMp f (x) M(q)g(x) for all x epsilon R-n if 2 < p, q < infinity and 1/p + 1/q = 1/2. Here M-# denotes the FeffermanStein sharp operator and M-p stands for the generalized Hardy-Littlewood maximal operator.