Application of Perron trees to geometric maximal operators

Abstract

We characterize the L p ( R 2 ) boundeness of the geometric maximal operator M a,b associated to the basis B a,b ( a, b > 0) which is composed of rectangles R whose eccentricity and orientation is of the form ( e R , ω R ) = (cid:18) 1 n a , π 4 n b (cid:19) for some n ∈ N ∗ . The proof involves generalized Perron trees , as constructed in [12].