Carleson measures, Riemann-Stieltjes and multiplication operators on a general family of function spaces

2013/07/18 by Jordi Pau, Pau, Jordi, Ruhan Zhao +1
Mathematics · #30H25 #47B38 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:30H25 #msc:47B38

paper · pdf · doi:10.48550/arxiv.1307.4900

26 pages

arxiv created 2013/07/18 · arxiv updated 2013/07/19

Abstract

Let μ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures μ such that the general family of spaces of analytic functions, F(p,q,s), which contain many classical function spaces, including the Bloch space, BMOA and the Q_s spaces, are embedded boundedly or compactly into the tent-type spaces T^∞_p,s(μ). The results are applied to characterize boundedness and compactness of Riemann-Stieltjes operators and multiplication operators on F(p,q,s).

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