Sharp $l^p$-improving estimates for the discrete paraboloid

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arxiv 2002.11758 v1 pith:7EBJP6II submitted 2020-02-26 math.CA

Shival Dasu , Ciprian Demeter , Bartosz Langowski This is my paper · ORCID

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keywords discreteestimatesimprovingparaboloidsharpalongaveragingdimensions

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abstract

We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.

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Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages
math.CA 2026-08 conditional novelty 6.0 of 10

Fixed-radius lattice sphere averages on Z^d satisfy the sharp l^p improving estimate down to the endpoint p=(d+2)/d for every d at least 4, with the optimal decay exponent.