Weighted Inequalities for Fractional Maximal Functions on the Infinite Rooted k-Ary Tree

Abstract

In this article, we introduce the fractional Hardy–Littlewood maximal function on the infinite rooted k-ary tree and study its weighted boundedness. We also provide examples of weights for which the fractional Hardy–Littlewood maximal function satisfies strong type (p, q) estimates on the infinite rooted k-ary tree.