Tent spaces over metric measure spaces under doubling and related assumptions

2013/05/10 by Alex Amenta, Amenta, Alex · 2 citations
Mathematics · #30L99 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.CA #math.FA #math.MG #msc:30L99 #msc:42B35

paper · pdf · doi:10.48550/arxiv.1305.2307

To appear in the Proceedings of IWOTA2012

arxiv created 2013/09/25 · arxiv updated 2013/09/26

Abstract

In this article, we define the Coifman-Meyer-Stein tent spaces T^p,q,α(X) associated with an arbitrary metric measure space (X,d,μ) under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, interpolation, and change of aperture theorems for the tent spaces. Because of the inherent technicalities in dealing with abstract metric measure spaces, most proofs are presented in full detail.

Cited by

• A new scale of function spaces characterizing homogeneous Besov spaces
• The Hardy spaces H^p_FIO(ℝⁿ) for Fourier integral operators for p<1

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