We consider the bilinear pseudo-differential operators with symbols in the bilinear Hörmander class \(BS_{\rho , \rho }^m ({\mathbb {R}}^n) \) for \(m \in {\mathbb {R}}\) and \(0 \le \rho < 1\). The aim of this paper is to discuss smoothness conditions for symbols to assure the boundedness from \(h^p \times h^q\) to \(h^r\) for \(1 \le r \le 2 \le p,q \le \infty \) satisfying \(1/p+1/q=1/r\), where \(h^\infty \) is replaced by the space bmo.

中文翻译：

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具有有限平滑度的奇异类符号的双线性伪微分算子

我们考虑双线性 Hörmander 类中符号的双线性伪微分算子\(BS_{\rho , \rho }^m ({\mathbb {R}}^n) \) for \(m \in {\mathbb { R}}\)和\(0 \le \rho < 1\)。本文的目的是讨论符号的平滑条件，以确保\(h^p \times h^q\)到\(h^r\)对于\(1 \le r \le 2 \le p ,q \le \infty \)满足\(1/p+1/q=1/r\)，其中\(h^\infty \)被空间bmo替换。