On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type

2016/10/13 by Gustavo Garrigós, Andreas Seeger, Garrigós, Gustavo +3 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #math.FA

paper · pdf · doi:10.48550/arxiv.1610.04145

13 pages

openalex publication_date 2016/10/13 · arxiv created 2017/02/28 · arxiv updated 2017/03/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We give an alternative proof of recent results by the authors on uniform boundedness of dyadic averaging operators in (quasi-)Banach spaces of Hardy-Sobolev and Triebel-Lizorkin type. This result served as the main tool to establish Schauder basis properties of suitable enumerations of the univariate Haar system in the mentioned spaces. The rather elementary proof here is based on characterizations of the respective spaces in terms of orthogonal compactly supported Daubechies wavelets.

Citations

• Some Maximal Inequalities

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