A_p weights on nonhomogeneous trees equipped with measures of exponential growth

2023/12/18 by Alessandro Ottazzi, Ottazzi, Alessandro, Federico Santagati +3
Mathematics · #05C05 #05C21 #43A99 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2312.11455

openalex publication_date 2023/12/18 · openalex created_date 2023/12/20 · openalex updated_date 2026/07/28

Abstract

This paper aims to study A_p weights in the context of a class of metric measure spaces with exponential volume growth, namely infinite trees with root at infinity equipped with the geodesic distance and flow measures. Our main result is a Muckenhoupt Theorem, which is a characterization of the weights for which a suitable Hardy--Littlewood maximal operator is bounded on the corresponding weighted L^p spaces. We emphasise that this result does not require any geometric assumption on the tree or any condition on the flow measure. We also prove a reverse Hölder inequality in the case when the flow measure is locally doubling. We finally show that the logarithm of an A_p weight is in BMO and discuss the connection between A_p weights and quasisymmetric mappings.

Related

• BMO spaces on weighted homogeneous trees
• H¹ and BMO spaces for exponentially decreasing measures on homogeneous trees
• Hardy spaces on weighted homogeneous trees
• Weighted discrete Hardy inequalities on trees and applications
• Fefferman-Stein inequalities for the Hardy-Littlewood maximal function on the infinite rooted k-ary tree