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Nuclear Pseudo-Differential Operators in Besov Spaces on Compact Lie Groups

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Abstract

In this work we establish the metric approximation property for Besov spaces defined on arbitrary compact Lie groups. As a consequence of this fact, we investigate trace formulae for nuclear Fourier multipliers on Besov spaces. Finally, we study the r-nuclearity, the Grothendieck–Lidskii formula and the (nuclear) trace of pseudo-differential operators in generalized Hörmander classes acting on periodic Besov spaces. We will restrict our attention to pseudo-differential operators with symbols of limited regularity.

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Acknowledgements

The author is indebted with Alexander Cardona for helpful comments on an earlier draft of this paper. The author would like to warmly thank the anonymous referee for his remarks and important advices leading to several improvements of the original paper.

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Authors and Affiliations

  1. Department of Mathematics, Universidad de los Andes, Bogotá, Colombia

    Duván Cardona

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  1. Duván Cardona
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Correspondence to Duván Cardona.

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Communicated by Michael Ruzhansky.

The author was supported by the Faculty of Sciences of the Universidad de los Andes, Project: Operadores en grupos de Lie compactos, 2016-I. No new data was created or generated during the course of this research.

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Cardona, D. Nuclear Pseudo-Differential Operators in Besov Spaces on Compact Lie Groups. J Fourier Anal Appl 23, 1238–1262 (2017). https://doi.org/10.1007/s00041-016-9512-8

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  • DOI: https://doi.org/10.1007/s00041-016-9512-8

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