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Singular integral operators on tent spaces

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Abstract

We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly appropriate condition on the kernel is time–space decay measured by off-diagonal estimates with various exponents.

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Author notes

  1. Pierre Portal

    Present address: Mathematical Sciences Institute, Australian National University, John Dedman Building, Acton, ACT, 0200, Australia

Authors and Affiliations

  1. Laboratoire de Mathématiques, UMR 8628, Université Paris-Sud, 91405, Orsay, France

    Pascal Auscher

  2. CNRS, 91405, Orsay, France

    Pascal Auscher

  3. Laboratoire de Mathématiques (UMR 6620), Université Blaise-Pascal (Clermont-Ferrand 2), Campus des Cézeaux, 63177, Aubière Cedex, France

    Christoph Kriegler

  4. LATP-UMR 7353, FST Saint-Jérôme, Université Aix-Marseille, 13397, Marseille Cédex 20, France

    Sylvie Monniaux

  5. Laboratoire Paul Painlevé, Université Lille 1, 59655, Villeneuve d’Ascq, France

    Pierre Portal

Authors
  1. Pascal Auscher
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  2. Christoph Kriegler
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  3. Sylvie Monniaux
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  4. Pierre Portal
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Corresponding author

Correspondence to Pascal Auscher.

Additional information

Christoph Kriegler acknowledges financial support from the Karlsruhe House of Young Scientists (KHYS).

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Auscher, P., Kriegler, C., Monniaux, S. et al. Singular integral operators on tent spaces. J. Evol. Equ. 12, 741–765 (2012). https://doi.org/10.1007/s00028-012-0152-4

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  • DOI: https://doi.org/10.1007/s00028-012-0152-4

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