论文标题
离散玻璃球形平均值的新界限
New bounds for discrete lacunary spherical averages
论文作者
论文摘要
我们表明，对于所有$ p> \ frac {d+1} {d-1} $，离散的球形最大函数在$ l^p（\ mathbb {z}^d）$上限制。我们的范围是在维度4中的新范围，在那里看来很少以一般的lacunary半径而闻名。我们的技术遵循Kesler-Lacey-Mena的技术，使用Kloosterman的精炼来改善多个地方的估计，从而导致维度4的总体改善。
We show that the discrete lacunary spherical maximal function is bounded on $l^p(\mathbb{Z}^d)$ for all $p >\frac{d+1}{d-1}$. Our range is new in dimension 4, where it appears that little was previously known for general lacunary radii. Our technique follows that of Kesler-Lacey-Mena, using the Kloosterman refinement to improve the estimates in several places, which leads to an overall improvement in dimension 4.
