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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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
Keywords
- Compact bilinear operators
- Real interpolation
- Convolution operators
- Commutators of bilinear Calderón–Zygmund operators