Revista Matemática Iberoamericana
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On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMORodolfo H. Torres and Qingying Xue (1) The University of Kansas, Lawrence, USA and University of California, Riverside, USA
(2) Beijing Normal University, China
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.
Keywords: Calder´on–Zygmund theory, singular integrals, commutators, bilinear operators, compact operators, bounded mean oscillation, CMO, VMO
Torres Rodolfo, Xue Qingying: On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO. Rev. Mat. Iberoam. Electronically published on January 3, 2020. doi: 10.4171/rmi/1156 (to appear in print)