Lipschitz spaces and Calderon-Zygmund operators associated to non-doubling measures

2002/12/20 by Jose Garcia-Cuerva, José Garcı́a-Cuerva, Garcia-Cuerva, Jose +2 · 1 citation
Mathematics · #42B20 26A33 47B38 47G10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA #msc:26A33 #msc:42B20 #msc:47B38 #msc:47G10

paper · pdf · doi:10.48550/arxiv.math/0212289

10 pages

arxiv created 2002/12/20 · openalex publication_date 2002/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of \R^d with an n-dimensional measure μ, we give several characterizations of Lipschitz spaces in terms of mean oscillations involving μ. We also show that Lipschitz spaces are preserved by those Calderon-Zygmund operators T associated to the measure μ for which T(1) is the Lipschitz class 0.

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