Triebel-Lizorkin Spaces on Metric Spaces via Hyperbolic Fillings

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Bonk , M , Saksman , E & Soto , T 2018 , ' Triebel-Lizorkin Spaces on Metric Spaces via Hyperbolic Fillings ' , Indiana University Mathematics Journal , vol. 67 , no. 4 , pp. 1625-1663 . https://doi.org/10.1512/iumj.2018.67.7282

Title: Triebel-Lizorkin Spaces on Metric Spaces via Hyperbolic Fillings
Author: Bonk, Mario; Saksman, Eero; Soto, Tomas
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018
Language: eng
Number of pages: 39
Belongs to series: Indiana University Mathematics Journal
ISSN: 0022-2518
URI: http://hdl.handle.net/10138/244922
Abstract: In this paper we give a new characterization of (homogeneous) Triebel-Lizorkin spaces F-p,q(s) (Z) in the smoothness range 0 <s <1 for a fairly general class of metric measure spaces . 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.
Subject: Function spaces
hyperbolic filling
metric measure space
Triebel-Lizorkin spaces
PARTIAL-DIFFERENTIAL-EQUATIONS
SOBOLEV SPACES
BESOV-SPACES
111 Mathematics
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