Optimal weak type estimates for dyadic-like maximal operators

2010/07/28 by Eleftherios Nikolidakis, Nikolidakis, Eleftherios
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1007.4982

26 pages

arxiv created 2010/07/28 · arxiv updated 2010/07/29

Abstract

We provide sharp weak estimates for the distribution function of Mϕwhen on ϕwe impose L1, Lq and Lp,1 restrictions. Here M is the dyadic maximal operator associated to a tree T on a non-atomic probability measure space.

Related

• Sharp weak type inequalities for the dyadic maximal operator
• Local lower norm estimates for dyadic maximal operators and related Bellman functions
• Restricted weak type inequalities for the one-sided Hardy-Littlewood maximal operators in higher dimensions
• An alternative approach to sharp L¹ estimates for the dyadic maximal operator
• Extremal problems related to maximal dyadic like operators