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Counterexamples to the \(L^p\)-Calderón–Zygmund estimate on open manifolds

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Abstract

We prove that for every \(m \in {\mathbb {N}}_{\ge 2}\) there exists a Riemannian manifold \({\mathcal {M}}\) of dimension m on which the \(L^p\)-Calderón–Zygmund estimate fails for all \(p \in ]1,\infty [\).

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Acknowledgements

This work has been done during Siran Li’s stay as a CRM–ISM postdoctoral fellow at Centre de Recherches Mathématiques, Université de Montréal and Institut des Sciences Mathématiques. The author would like to thank these institutions and Dima Jakobson for their hospitality, and to Concordia University and Galia dafni for providing a great work environment. Siran Li is indebted to Jianchun Chu for insightful discussions on problems in global analysis, and to Michele Rimoldi, Debora Impera, and Giona Veronelli for communications on the work [7]. Moreover, the author thanks the anonymous referee for his/her careful reading and insightful remarks.

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  1. Department of Mathematics, Rice University, MS 136, P.O. Box 1892, Houston, TX, 77251-1892, USA

    Siran Li

  2. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, QC, H3A 0B9, Canada

    Siran Li

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  1. Siran Li
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Correspondence to Siran Li.

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Li, S. Counterexamples to the \(L^p\)-Calderón–Zygmund estimate on open manifolds. Ann Glob Anal Geom 57, 61–70 (2020). https://doi.org/10.1007/s10455-019-09688-3

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  • DOI: https://doi.org/10.1007/s10455-019-09688-3

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