2021
DOI: 10.48550/arxiv.2112.05494
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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… Show more

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“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%