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$\ell^p(\mathbb{Z}^d)$-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Means, Revisited. (arXiv:1809.06468v1 [math.CA])

来源于:arXiv
We prove an expanded range of $\ell ^{p}(\mathbb{Z}^d)$-improving properties and sparse bounds for discrete spherical maximal means in every dimension $d\geq 6$. Essential elements of the proofs are bounds for high exponent averages of Ramanujan and restricted Kloosterman sums. 查看全文>>