COMPACTNESS OF THE COMMUTATOR OF BILINEAR FOURIER MULTIPLIER OPERATOR
COMPACTNESS OF THE COMMUTATOR OF BILINEAR FOURIER MULTIPLIER OPERATOR
Let $b_1, b_2 \in {\rm CMO}(\mathbb{R}^n)$ and $T_{\sigma}$ be the bilinear Fourier multiplier operator with associated multiplier $\sigma$ satisfies the Sobolev regularity that $\sup_{\kappa\in \mathbb{Z}}\|\sigma_{\kappa}\|_{W^{s_1,\,s_2}(\mathbb{R}^{2n})}\lt \infty$ for some $s_1,\,s_2\in (n/2,\,n]$. In this paper, it is proved that the commutator defined by $$T_{\sigma,\,\vec{b}}(f_1,\,f_2)(x) = b_1(x) T_{\sigma}(f_1,\,f_2)(x) - T_{\sigma}(b_1 f_1,\,f_2)(x) + b_2(x) …