A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition

2000/02/25 by Xavier Tolsa, Tolsa, Xavier · 2 citations
Mathematics · #42B20 #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:42B20

paper · pdf · doi:10.48550/arxiv.math/0002221

10 pages

arxiv created 2000/02/25 · openalex publication_date 2000/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a doubling measure μ on R^d, it is a classical result of harmonic analysis that Calderon-Zygmund operators which are bounded in L²(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderon-Zygmund decomposition adapted to the non doubling situation.

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• Sparse domination via the Calderón-Zygmund decomposition: the example of Dini-smooth kernels
• Harmonic Bergman spaces on locally finite trees

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