Title: The Universal maximal operator on special classes of functions

Authors: Javier Duoandikoetxea and Virginia Naibo

Issue: Volume 54 (2005), Issue 5, 1351-1370

Abstract: We prove pointwise inequalities for the maximal operator over all the directions in $\mathbb{R}^{n}$ when acting on $l^q$-radial functions and on product functions. From these inequalities we deduce boundedness results on $L^{p}$ for $p$ greater than $n$; these can be applied to other operators, in particular to the Kakeya maximal operator.