2000/02/18 by Xavier Tolsa, Tolsa, Xavier
Mathematics · #42B20 #42B30 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CA #math.CV #math.FA #msc:42B20 #msc:42B30
paper · pdf · doi:10.48550/arxiv.math/0002152
58 pages
arxiv created 2000/02/18 · openalex publication_date 2000/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a Radon measure μ on Rd, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when μ is doubling remain valid for the space BMO introduced in this paper, without assuming μ doubling. For instance, Calderon-Zygmund operators which are bounded in L2 are bounded from L^∞ into the new BMO space. Moreover, a John-Nirenberg inequality is satisfied, and the predual of BMO is an atomic space H1. Using a sharp maximal function it is proved that operators bounded from L^∞ into BMO and from H1 into L1 are also bounded on Lp, 1