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Compactness properties of commutators of bilinear fractional integrals

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Abstract

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.

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Notes

  1. The notion \(CMO\) for this space is not uniformly used throughout the literature. See [1] for remarks and references about this notation.

  2. We actually obtain estimates for these terms that slightly improve on the corresponding ones for \({\upalpha }=0\) in [1].

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Acknowledgments

This work was positively impacted by the interactions that occurred during Bényi’s and Torres’ stay at the Erwin Schrödinger Institute (ESI), Vienna, Austria, for the special semester on Modern Methods of Time-Frequency Analysis II. They wish to express their gratitude to the ESI and the organizers of the event for their support and warm hospitality.

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Authors and Affiliations

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

    Árpád Bényi

  2. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain

    Wendolín Damián

  3. Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487, USA

    Kabe Moen

  4. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Rodolfo H. Torres

Authors
  1. Árpád Bényi
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  2. Wendolín Damián
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  3. Kabe Moen
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  4. Rodolfo H. Torres
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Corresponding author

Correspondence to Árpád Bényi.

Additional information

Á. B. partially supported by a grant from the Simons Foundation (No. 246024). K. M. and R. H. T. partially supported by NSF Grants 1201504 and 1069015, respectively.

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Bényi, Á., Damián, W., Moen, K. et al. Compactness properties of commutators of bilinear fractional integrals. Math. Z. 280, 569–582 (2015). https://doi.org/10.1007/s00209-015-1437-4

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  • DOI: https://doi.org/10.1007/s00209-015-1437-4

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