Authors: Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Compactness of Riemann-Stieltjes operators between F(p,q,s) spaces and α-Bloch spaces
Journal: Publicationes Mathematicae
Volume: 72
Issue: 1-2
First page: 111
Last page: 128
Issue Date: 19-Mar-2008
Rank: M23
ISSN: 0033-3883
Let H(B) denote the space of all holomorphic functions on the unit ball B ⊂ ℂ n. In this paper we investigate the following integral operators T g(f)(z) = ∫ 01 f(tz)ℜg(tz)dt/t and L g(f)(z) = ∫ 01 Rf(tz)g(tz) dt/t, f ∈ H(B), z ∈ B, where g ∈ H(B) and ℜh(z) = Σ j=1n z j∂h/∂z j(z) is the radial derivative of h. The operator T g can be considered as an extension of the Cesàro operator on the unit disk. The compactness of the operators T g and L g between the general function space F(p, q, s), which includes the Hardy space, Bergman space, Bloch space, and Q p space, and the α-Bloch space are discussed.
Keywords: α-Bloch space | Compact | F(p, q, s) space | Riemann-Stieltjes operator
Publisher: Kossuth Lajos Tudomanyegyetem

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