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Singular integral operators on tent spaces over spaces of homogeneous type: Fefferman–Stein box maximal functions and pointwise Carleson type estimates

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Abstract

In this article we generalize the singular integral operator theory on weighted tent spaces to spaces of homogeneous type. This generalization of operator theory is in the spirit of C. Fefferman and Stein since we use some auxiliary functionals on tent spaces which play roles similar to the Fefferman–Stein sharp and box maximal functions in the Lebesgue space setting. Our contribution in this operator theory is twofold: for singular integral operators (including maximal regularity operators) on tent spaces pointwise Carleson type estimates are proved and this recovers known results; on the underlying space no extra geometrical conditions are needed and this could be useful for future applications to parabolic problems in rough settings.

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Acknowledgements

The author is indebted to the referee for some helpful comments.

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Authors and Affiliations

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

    Yi Huang

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Yi Huang

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  1. Yi Huang
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Correspondence to Yi Huang.

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This research is supported in part by the ANR Project “Harmonic Analysis at its Boundaries”, ANR-12-BS01-0013-01. The author would like to thank Professor Pascal Auscher for introducing him to the topic “operator theory on tent spaces”.

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Huang, Y. Singular integral operators on tent spaces over spaces of homogeneous type: Fefferman–Stein box maximal functions and pointwise Carleson type estimates. Arch. Math. 111, 633–646 (2018). https://doi.org/10.1007/s00013-018-1235-4

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  • DOI: https://doi.org/10.1007/s00013-018-1235-4

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