Research Output
Lp→Lq bounds for spherical maximal operators
  Let f∈Lp(Rd), d≥3, and let Atf(x) be the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.

  • Type:

    Article

  • Date:

    05 June 2020

  • Publication Status:

    Published

  • Publisher

    Springer Science and Business Media LLC

  • DOI:

    10.1007/s00209-020-02546-0

  • Cross Ref:

    10.1007/s00209-020-02546-0

  • ISSN:

    0025-5874

  • Funders:

    Historic Funder (pre-Worktribe)

Citation

Anderson, T., Hughes, K., Roos, J., & Seeger, A. (2021). Lp→Lq bounds for spherical maximal operators. Mathematische Zeitschrift, 297(3-4), 1057-1074. https://doi.org/10.1007/s00209-020-02546-0

Authors

Keywords

Lp -improving estimates, Spherical maximal functions, Minkowski dimension, Assouad dimension, Assouad spectrum, Sparse domination

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