We show quantitative (in terms of the radius) \(l^p\)-improving estimates for the discrete spherical averages along the primes. These averaging operators were defined in [1] and are discrete, prime variants of Stein’s spherical averages. The proof uses a precise decomposition of the Fourier multiplier.

中文翻译：

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$$ l ^ p $$ lp定量-沿素数的离散球形平均数的改进

我们显示了定量的（就半径而言）\（l ^ p \）-改进了沿素数的离散球形平均值的估计。这些平均算子在[1]中定义，并且是斯坦因球均值的离散素数变体。该证明使用傅立叶乘数的精确分解。