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. 2020 Mathematics Subject Classification. 42B25, 05C63. Key words and phrases. Infinite rooted k-ary tree, fractional Hardy-Littlewood maximal function, weights. E.R. is partially supported by grants UBACyT 20020170200057BA and PIP (CONICET) 11220110101018.

Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted $L^p$ maximal inequalities

“…In the last years the study of harmonic analysis in the homogeneous trees has turned to take great interest. Heat and Poisson semigroups ( [24] and [31]), Poincaré and Hardy inequalities [5], Hardy and BMO spaces ( [3,4,7]), nondoubling flow measures ( [25,26]), uncertainty principles ( [15]), Carleson measures ( [12]), special multipliers ( [8]) and maximal functions ( [14,18,28,29]) are some of the topics that have being recently studied in this setting.…”