BMO spaces on weighted homogeneous trees

2020/06/04 by Laura Arditti, Arditti, Laura, Anita Tabacco +3
Mathematics · #05C05 #30H35 #42B30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:05C05 #msc:30H35 #msc:42B30

paper · pdf · doi:10.48550/arxiv.2006.02693

14 pages

arxiv created 2020/06/04 · arxiv updated 2020/06/05

Abstract

We consider an infinite homogeneous tree \mathcal V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (\mathcal V,d,μ) is nondoubling and of exponential growth, hence the classical theory of Hardy and BMO spaces does not apply in this setting. We introduce a space BMO(μ) on (\mathcal V,d,μ) and investigate some of its properties. We prove in particular that BMO(μ) can be identified with the dual of a Hardy space H¹(μ) introduced in a previous work and we investigate the sharp maximal function related with BMO(μ).

Related

• Hardy spaces on weighted homogeneous trees
• H¹ and BMO spaces for exponentially decreasing measures on homogeneous trees
• A_p weights on nonhomogeneous trees equipped with measures of exponential growth
• Remarks about Hardy inequalities on metric trees
• Uniformly continuous maps between ends of R-trees