Weighted Compact Commutator of Bilinear Fourier Multiplier Operator

Let T-sigma be the bilinear Fourier multiplier operator with associated multiplier a satisfying the Sobolev regularity that sup(kappa is an element of Z)parallel to sigma(kappa)parallel to(Ws) ((R2n)) < infinity for some s is an element of (n, 2n]. In KEZ this paper, it is proved that the commutator generated by T-sigma and CMO(R-n) functions is a compact operator from L-p1 (R-n, w(1)) x L-p2 (R-n, w(2)) to L-p (R-n, v(<(w)over right arrow>)) for appropriate indices p(1), p(2), p is an element of (1, infinity) with 1/p = 1/p(1) + 1/p(2) and weights w(1), w(2) such that (w) over right arrow = (w(1), w(2)) is an element of A(p/(t) over right arrow)(R-2n).