It is known that the compactness of the commutators of point-wise multiplication with bilinear homogeneous Calderón–Zygmund operators acting on product of Lebesgue spaces is characterized by the multiplying function being in the space CMO. This space is the closure in BMO of its subspace of smooth functions with compact support. It is shown in this work that for bilinear Calderón–Zygmund operators arising from smooth (inhomogeneous) bilinear Fourier multipliers or bilinear pseudodifferential operators, one can actually consider multiplying functions in a new subspace of BMO larger than CMO.

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关于乘法和双线性伪微分算子的交换子的紧致性和BMO的新子空间

众所周知，作用于Lebesgue空间乘积的具有双线性齐次Calderón–Zygmund算子的逐点乘法换向器的紧致性以空间CMO中的乘法函数为特征。该空间是BMO封闭的，具有紧凑功能的平滑功能子空间的封闭空间。这项工作表明，对于由光滑（不均匀）双线性傅里叶乘法器或双线性伪微分算子产生的双线性Calderón-Zygmund算子，实际上可以考虑在比CMO大的BMO新子空间中使用乘法函数。