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Real Interpolation of Compact Bilinear Operators

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Abstract

We establish an analog for bilinear operators of the compactness interpolation result for bounded linear operators proved by Cwikel and Cobos, Kühn and Schonbek. We work with the assumption that \(T:(A_0+A_1) \times (B_0+B_1) \longrightarrow E_0+E_1\) is bounded, but we also study the case when this does not hold. Applications are given to compactness of convolution operators and compactness of commutators of bilinear Calderón–Zygmund operators.

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Acknowledgements

The authors would like to thank the referees for their comments which have led to improve the paper. The authors have been supported in part by the Spanish Ministerio de Economía y Competitividad (MTM2013-42220-P).

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Authors and Affiliations

  1. Sección Departamental de Matemática Aplicada, Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Luz M. Fernández-Cabrera

  2. Departamento de Matemática Aplicada I, Escuela de Ingeniería Industrial, Universidad de Vigo, 36200, Vigo, Spain

    Antón Martínez

Authors
  1. Luz M. Fernández-Cabrera
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  2. Antón Martínez
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Correspondence to Luz M. Fernández-Cabrera.

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Communicated by Winfried Sickel.

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Fernández-Cabrera, L.M., Martínez, A. Real Interpolation of Compact Bilinear Operators. J Fourier Anal Appl 24, 1181–1203 (2018). https://doi.org/10.1007/s00041-017-9561-7

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  • DOI: https://doi.org/10.1007/s00041-017-9561-7

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