We consider bilinear pseudo-differential operators whose symbols may have a sub-exponential growth at infinity, together with all their derivatives. It is proved that those symbol classes can be described by the means of the short-time Fourier transform and modulation spaces. Our first main result is the invariance property of the corresponding bilinear operators. Furthermore, we prove the continuity of such operators when acting on modulation spaces. As a consequence, we derive their continuity on anisotropic Gelfand–Shilov type spaces.

中文翻译：

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具有Gevrey–Hörmander符号的双线性伪微分算子

我们考虑其符号可能在无穷大处具有次指数增长的双线性伪微分算子，以及它们的所有导数。证明了可以通过短时傅立叶变换和调制空间来描述这些符号类别。我们的第一个主要结果是相应双线性算子的不变性。此外，我们证明了在调制空间上作用时此类算子的连续性。结果，我们得出了它们在各向异性Gelfand–Shilov类型空间上的连续性。