论文标题
Kakeya型几何最大操作员
Kakeya-type sets for Geometric Maximal Operators
论文作者
论文摘要
Given a family G of rectangles, to which one associates a tree [G], one defines a natural number $λ$ [G] called its analytic split and satisfying, for all 1 < p < $\infty$ log($λ$ [G]) p MG p p where MG is the Hardy-Littlewood type maximal operator associated to the family G. As an application, we completely characterize the boundeness of planar rarefied directional maximal operators在1 <p <$ \ infty $上。确切地说，如果$ω$在[0，$π$ 4）中是一组任意的角度，我们证明，方向基础r $ω$的任何稀有基础B会产生比方向最大运算符M $ m $ m $ m $ m $ m $ m $ m $ mb的操作员MB，对于1 <p <p <$ f $ \ iffty $。
Given a family G of rectangles, to which one associates a tree [G], one defines a natural number $λ$ [G] called its analytic split and satisfying, for all 1 < p < $\infty$ log($λ$ [G]) p MG p p where MG is the Hardy-Littlewood type maximal operator associated to the family G. As an application, we completely characterize the boundeness of planar rarefied directional maximal operators on L p for 1 < p < $\infty$. Precisely, if $Ω$ is an arbitrary set of angles in [0, $π$ 4), we prove that any rarefied basis B of the directional basis R $Ω$ yields an operator MB that has the same L p-behavior than the directional maximal operator M $Ω$ for 1 < p < $\infty$.
