All Outputs (2)

Lp-improving for discrete spherical averages (2020)
Journal Article
Hughes, K. (2020). Lp-improving for discrete spherical averages. Annales Henri Lebesgue, 3, 959-980. https://doi.org/10.5802/ahl.50

We initiate the theory of -improving inequalities for arithmetic averages over hypersurfaces and their maximal functions. In particular, we prove -improving estimates for the discrete spherical averages and some of their generalizations. As an applic... Read More about Lp-improving for discrete spherical averages.

Lp→Lq bounds for spherical maximal operators (2020)
Journal Article
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

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 o... Read More about Lp→Lq bounds for spherical maximal operators.