论文标题
bs_ {1,1}^m $ in triebel-lizorkin spaces带有关键sobolev index的双线性伪差操作员带有符号的符号
Bilinear pseudodifferential operators with symbol in $BS_{1,1}^m$ on Triebel-Lizorkin spaces with critical Sobolev index
论文作者
论文摘要
在本文中，当两个参数都属于$ f_ {p，q}^{n/p}（n/p}（\ MathBb {r}^n）$时，我们获得了$ bs_ {1,1}^m $ sumply bs $ bs_ {1,1}^m $ sumbly bs $ bs_ {1,1}^m $的新估计值的新估计值。不等式是由于经典sobolev嵌入$ f^{n/p} _ { $ \ mathrm {bmo}（\ mathbb {r}^n）$由适当的子空间，其中包含$ l^\ infty（\ mathbb {r}^n）$。作为一个应用程序，我们在$ f_ {p，q}^{n/p}上研究功能的产物（\ mathbb {r}^n）$当$ 1 <p <\ infty $，其中这些空间不可能是多重代数。
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 $F^{n/p}_{p,q}(\mathbb{R}^n)\hookrightarrow\mathrm{bmo}(\mathbb{R}^n)$, where we replace $\mathrm{bmo}(\mathbb{R}^n)$ 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.
