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Smoothing of Commutators for a Hörmander Class of Bilinear Pseudodifferential Operators

Journal of Fourier Analysis and Applications volume 20, pages 282–300 (2014)Cite this article

Abstract

Commutators of bilinear pseudodifferential operators with symbols in the Hörmander class \(BS_{1, 0}^{1}\) and multiplication by Lipschitz functions are shown to be bilinear Calderón-Zygmund operators. A connection with a notion of compactness in the bilinear setting for the iteration of the commutators is also made.

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Authors and Affiliations

  1. Department of Mathematics, Western Washington University, 516 High St, Bellingham, WA, 98225, USA

    Árpád Bényi

  2. School of Mathematics, The University of Edinburgh and The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

    Tadahiro Oh

Authors
  1. Árpád Bényi
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  2. Tadahiro Oh
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Corresponding author

Correspondence to Árpád Bényi.

Additional information

Communicated by Loukas Grafakos.

This work is partially supported by a grant from the Simons Foundation Grant (No. 246024 to Árpád Bényi). The second author acknowledges support from an AMS-Simons Travel Grant.

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Bényi, Á., Oh, T. Smoothing of Commutators for a Hörmander Class of Bilinear Pseudodifferential Operators. J Fourier Anal Appl 20, 282–300 (2014). https://doi.org/10.1007/s00041-013-9312-3

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  • DOI: https://doi.org/10.1007/s00041-013-9312-3

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