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Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex

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Abstract

We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors’ recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat kernel bounds are shown in the context of classical Jacobi expansions, on a ball and on a simplex. These results are more precise than the qualitatively sharp Gaussian estimates proved recently by several authors.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656, Warsaw, Poland

    Adam Nowak

  2. Mathematical Sciences, University of Gothenburg, Göteborg, Sweden

    Peter Sjögren

  3. Mathematical Sciences, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Peter Sjögren

  4. Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA

    Tomasz Z. Szarek

  5. Mathematical Institute, University of Wrocław, Plac Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Tomasz Z. Szarek

Authors
  1. Adam Nowak
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  2. Peter Sjögren
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  3. Tomasz Z. Szarek
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Correspondence to Tomasz Z. Szarek.

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Communicated by Loukas Grafako.

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Research supported by the National Science Centre of Poland within the Project OPUS 2017/27/B/ST1/01623. Tomasz Z. Szarek was supported also by the Foundation for Polish Science via the START Scholarship.

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Nowak, A., Sjögren, P. & Szarek, T.Z. Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex. Math. Ann. 381, 1455–1476 (2021). https://doi.org/10.1007/s00208-021-02185-8

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  • DOI: https://doi.org/10.1007/s00208-021-02185-8

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