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Tent space boundedness via extrapolation

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Abstract

We study the action of operators on tent spaces such as maximal operators, Calderón–Zygmund operators, Riesz potentials. We also consider singular non-integral operators. We obtain boundedness as an application of extrapolation methods in the Banach range. In the non Banach range, boundedness results for Calderón–Zygmund operators follow by using an appropriate atomic theory. We end with some consequences on amalgam spaces.

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Authors and Affiliations

  1. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405, Orsay, France

    Pascal Auscher

  2. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera, 13-15, 28049, Madrid, Spain

    Cruz Prisuelos-Arribas

Authors
  1. Pascal Auscher
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  2. Cruz Prisuelos-Arribas
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Correspondence to Pascal Auscher.

Additional information

Pascal Auscher was partially supported by the ANR project “Harmonic Analysis at its Boundaries”, ANR-12-BS01-0013. Cruz Prisuelos-Arribas has been supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Agreement No. 615112 HAPDEGMT.

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Auscher, P., Prisuelos-Arribas, C. Tent space boundedness via extrapolation. Math. Z. 286, 1575–1604 (2017). https://doi.org/10.1007/s00209-016-1814-7

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