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ℓp(ℤd)-Improving properties and sparse bounds for discrete spherical maximal averages

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Abstract

We exhibit a range of ℓP(ℤD)-improving properties for the discrete spherical maximal average in every dimension d ≥ 5. These improving properties are then used to establish sparse bounds, which extend the discrete maximal theorem of Magyar, Stein, and Wainger to weighted spaces. In particular, the sparse bounds imply that in every dimension d ≥ 5 the discrete spherical maximal average is a bounded map from ℓ2(w) into ℓ2(w) provided \({w^{{d \over {d - 4}}}}\) belongs to the Muckenhoupt class A2.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Robert Kesler

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  1. Robert Kesler
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Correspondence to Robert Kesler.

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Kesler, R. ℓp(ℤd)-Improving properties and sparse bounds for discrete spherical maximal averages. JAMA 143, 151–178 (2021). https://doi.org/10.1007/s11854-021-0150-y

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  • DOI: https://doi.org/10.1007/s11854-021-0150-y

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