Application of Perron trees to geometric maximal operators
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 1-13
MSC: Primary 42B25.
DOI: 10.4064/cm8693-8-2022
Published online: 29 September 2022
Abstract
We characterize the 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 ,\omega _R \right ) = \left ( \frac {1}{n^a} , \frac {\pi }{4n^b} \right ) for some n \in \mathbb {N}^*. The proof involves generalized Perron trees, as constructed by Hare and Röning [J. Fourier Anal. Appl. 4 (1998)].