Interpolation and embeddings of weighted tent spaces

2015/09/18 by Alex Amenta, Amenta, Alex · 2 citations
Mathematics · #42B35 (Primary) #46E30 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:42B35 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1509.05699

Final version, to appear in the Journal of Fourier Analysis and Applications

arxiv created 2016/12/20 · arxiv updated 2016/12/21

Abstract

Given a metric measure space X, we consider a scale of function spaces T^p,q_s(X), called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on X we identify some associated interpolation spaces, in particular certain real interpolation spaces. These are identified with a new scale of function spaces, which we call Z-spaces, that have recently appeared in the work of Barton and Mayboroda on elliptic boundary value problems with boundary data in Besov spaces. We also prove Hardy--Littlewood--Sobolev-type embeddings between weighted tent spaces.

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

Related

• A new scale of function spaces characterizing homogeneous Besov spaces
• Weighted tent spaces with Whitney averages: factorization, interpolation and duality
• Interpolation and Sampling in Analytic Tent Spaces
• Tent spaces over metric measure spaces under doubling and related assumptions
• Weighted fractional Sobolev spaces as interpolation spaces in bounded domains