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Commutators of Bilinear Pseudodifferential Operators and Lipschitz Functions

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Abstract

Commutators of bilinear pseudodifferential operators and the operation of multiplication by a Lipschitz function are studied. The bilinear symbols of the pseudodifferential operators considered belong to classes that are shown to properly contain certain bilinear Hörmander classes of symbols of order one. The corresponding commutators are proved to be bilinear Calderón–Zygmund operators.

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Acknowledgements

The authors initiated this collaboration while visiting the Pacific Institute for the Mathematical Sciences in June 2015, during the Western International Workshop on Harmonic Analysis and PDE. They thank the institute and the organizers of the workshop for their hospitality.

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Authors and Affiliations

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

    Árpád Bényi

  2. Department of Mathematics, Kansas State University, 138 Cardwell Hall, 1228 N. 17th Street, Manhattan, KS, 66506, USA

    Virginia Naibo

Authors
  1. Árpád Bényi
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  2. Virginia Naibo
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Corresponding author

Correspondence to Virginia Naibo.

Additional information

Communicated by Rodolfo H. Torres.

The first author is partially supported by a grant from the Simons Foundation (No. 246024). The second author is supported by NSF under Grant DMS 1500381.

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Bényi, Á., Naibo, V. Commutators of Bilinear Pseudodifferential Operators and Lipschitz Functions. J Fourier Anal Appl 24, 759–779 (2018). https://doi.org/10.1007/s00041-016-9519-1

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  • DOI: https://doi.org/10.1007/s00041-016-9519-1

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