In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class \(BS_{1,1}^m\), when both arguments belong to Triebel-Lizorkin spaces of the type \(F_{p,q}^{n/p}({\mathbb {R}}^n)\). The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding \(F^{n/p}_{p,q}({\mathbb {R}}^n)\hookrightarrow \textrm{bmo}({\mathbb {R}}^n)\), where we replace \(\textrm{bmo}({\mathbb {R}}^n)\) by an appropriate subspace which contains \(L^\infty ({\mathbb {R}}^n)\). As an application, we study the product of functions on \(F_{p,q}^{n/p}({\mathbb {R}}^n)\) when \(1<p<\infty \), where those spaces fail to be multiplicative algebras.

在本文中，当两个参数都属于类型为\ (F_{p,q}^ {n/p}({\mathbb {R}}^n)\)。这些不等式是通过对经典 Sobolev 嵌入\(F^{n/p}_{p,q}({\mathbb {R}}^n)\hookrightarrow \textrm{bmo}({ \mathbb {R}}^n)\) ，我们用包含\(L^\infty ({\ mathbb {R}}^n)\)。作为一个应用，我们研究函数在\(F_{p,q}^{n/p}({\mathbb {R}}^n)\) 上的乘积，当\(1<p<\infty \)，其中这些空间不是乘法代数。