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.
Sharp $l^p$-improving estimates for the discrete paraboloid
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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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math.CA 1years
2026 1verdicts
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Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages
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.