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.
Cite this article
Rodolfo H. Torres, Qingying Xue, On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 939–956DOI 10.4171/RMI/1156