Triebel-Lizorkin spaces on metric spaces via hyperbolic fillings

2014/11/21 by Bonk, Mario, Saksman, Eero, Soto, Tomás · 1 citation
#42B35 (Primary) #46E35 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1411.5906

Abstract

We give a new characterization of (homogeneous) Triebel-Lizorkin spaces \mathcal F^s_p,q(Z) in the smoothness range 0 < s < 1 for a fairly general class of metric measure spaces Z. The characterization uses Gromov hyperbolic fillings of Z. This gives a short proof of the quasisymmetric invariance of these spaces in case Z is Q-Ahlfors regular and sp = Q > 1. We also obtain first results on complex interpolation for these spaces in the framework of doubling metric measure spaces.

Cited by

• Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings

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