论文标题
将Perron树应用于几何最大运算符
Application of Perron Trees to Geometric Maximal Operators
论文作者
论文摘要
We characterize the $L^p(\mathbb{R}^2)$ boundeness of the geometric maximal operator $M_{a,b}$ associated to the basis $\mathcal{B}_{a,b}$ ($a,b > 0$) which is composed of rectangles $R$ whose eccentricity and orientation is of the form $$\left( e_R ，ω_r\ right）= \ left（\ frac {1} {n^a}，\fracπ{4n^b} \ right）$$ in \ in \ mathbb {n}^*$ in \ mathbb in \ mathbb in \ mathbb in。证明涉及\ textit {概括的perron树}，如\ cite {kathryn jan}中构建。
We characterize the $L^p(\mathbb{R}^2)$ boundeness of the geometric maximal operator $M_{a,b}$ associated to the basis $\mathcal{B}_{a,b}$ ($a,b > 0$) which is composed of rectangles $R$ whose eccentricity and orientation is of the form $$\left( e_R ,ω_R \right) = \left( \frac{1}{n^a} , \fracπ{4n^b} \right)$$ for some $n \in \mathbb{N}^*$. The proof involves \textit{generalized Perron trees}, as constructed in \cite{KATHRYN JAN}.
