A+ CATEGORY SCIENTIFIC UNIT

Application of Perron trees to geometric maximal operators

Anthony Gauvan Colloquium Mathematicum MSC: Primary 42B25. DOI: 10.4064/cm8693-8-2022 Published online: 29 September 2022

Abstract

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 $$ \left ( e_R ,\omega _R \right ) = \left ( \frac {1}{n^a} , \frac {\pi }{4n^b} \right ) $$ for some $n \in \mathbb {N}^*$. The proof involves generalized Perron trees, as constructed by Hare and Röning [J. Fourier Anal. Appl. 4 (1998)].

Authors

  • Anthony GauvanInstitut de Mathématiques d’Orsay
    307 rue Michel Magat
    Orsay 91400, France
    e-mail

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