2023 AN α-NUMBER CHARACTERIZATION OF Lp SPACES ON UNIFORMLY RECTIFIABLE SETS
Jonas Azzam, Damian Dąbrowski
Author Affiliations +
Publ. Mat. 67(2): 819-850 (2023). DOI: 10.5565/PUBLMAT6722313

Abstract

We give a characterization of Lp(σ) for uniformly rectifiable measures σ using Tolsa’s α-numbers, by showing, for 1<p< and fLp(σ), that

fLp(σ)~(0(αfσ(x,r)+|f|x,rασ(x,r))2drr)12Lp(σ).

Citation

Download Citation

Jonas Azzam. Damian Dąbrowski. "AN α-NUMBER CHARACTERIZATION OF Lp SPACES ON UNIFORMLY RECTIFIABLE SETS." Publ. Mat. 67 (2) 819 - 850, 2023. https://doi.org/10.5565/PUBLMAT6722313

Information

Received: 29 July 2021; Revised: 5 May 2022; Published: 2023
First available in Project Euclid: 29 June 2023

MathSciNet: MR4609021
zbMATH: 07720480
Digital Object Identifier: 10.5565/PUBLMAT6722313

Subjects:
Primary: 28A75
Secondary: 42B25 , 46E30

Keywords: Lp spaces , quantitative rectifiability , uniformly rectifiable sets , α-numbers

Rights: Copyright © 2023 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
32 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.67 • No. 2 • 2023
Back to Top