The Q_p Carleson Measure Problem

2007/08/27 by J. Xiao, Jie Xiao, Xiao, Jie
Mathematics · #28 #30C #30H #47B #47G #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CV #math.FA #msc:28 #msc:30C #msc:30H #msc:47B #msc:47G

paper · pdf · doi:10.48550/arxiv.0708.3621

12 pages

arxiv created 2007/08/27 · openalex publication_date 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ be a nonnegative Borel measure on the open unit disk \mathbbD⊂ℂ. This note shows how to decide that the Möbius invariant space Q_p, covering BMOA and B, is boundedly (resp., compactly) embedded in the quadratic tent-type space T^∞_p(μ). Interestingly, the embedding result can be used to determine the boundedness (resp., the compactness) of the Volterra-type and multiplication operators on Q_p.

Citations

• Some new function spaces and their applications to Harmonic analysis

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