Application of Perron trees to geometric maximal operators
Anthony Gauvan · Colloquium Mathematicum · 2022
We characterize the $L^p(\mathbb R^2)$ boundedness of the geometric maximal operator $M_{a,b}$ associated to the basis $\mathcal B_{a,b}$ ($a,b \gt 0$) which is composed of rectangles $R$ whose eccentricity and orientation are of the form $$ \left ( e_R ,