论文标题
部分可观测时空混沌系统的无模型预测
Nikodym sets and maximal functions associated with spheres
论文作者
论文摘要
我们研究Nikodym集和相关最大功能的球形类似物。特别是，我们证明了与球体相关的Nikodym最大功能的尖锐$ l^p $估计。作为推论，任何针对球体设置的Nikodym都必须具有完整的Hausdorff尺寸。此外，我们考虑一类最大函数，其中包含球形最大函数作为特殊情况。我们表明，这些最大函数的$ l^p $估计值可以从相对于分形测量的波动方程的局部平滑估计来推测。
We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp $L^p$-estimates for Nikodym maximal functions associated with spheres. As a corollary, any Nikodym set for spheres must have full Hausdorff dimension. In addition, we consider a class of maximal functions which contains the spherical maximal function as a special case. We show that $L^p$-estimates for these maximal functions can be deduced from local smoothing estimates for the wave equation relative to fractal measures.
