2015
DOI: 10.1016/j.jmaa.2015.01.010
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Composition operators on weighted Bergman spaces of Dirichlet series

Abstract: We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a sufficient condition of compactness is obtained using the notion of Carleson's measure. Mathematics Subject Classification.Primary: 47B33 -Secondary: 46E15.

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Cited by 17 publications
(25 citation statements)
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“…Assume that w n 1. There exists a function F ∈ H w such that (1) For almost all χ ∈ T ∞ , F χ converges in C 0 and cannot be analytically continued to any larger domain; (2) For at least one χ ∈ T ∞ , F χ converges in C 1/2 and cannot be analytically continued to any larger domain.…”
Section: Proof Of Theoremmentioning
confidence: 99%
See 1 more Smart Citation
“…Assume that w n 1. There exists a function F ∈ H w such that (1) For almost all χ ∈ T ∞ , F χ converges in C 0 and cannot be analytically continued to any larger domain; (2) For at least one χ ∈ T ∞ , F χ converges in C 1/2 and cannot be analytically continued to any larger domain.…”
Section: Proof Of Theoremmentioning
confidence: 99%
“…The author is supported by the Research Council of Norway grant 227768. 1 We observe from the proof of this extension (see [2,Theorem 1]) that D α are actually mapped into weighted Hilbert spaces that consist of Dirichlet series F (s) = ∞ n=1 a n n −s satisfying…”
Section: Introductionmentioning
confidence: 99%
“…3 is not zero. By way of contradiction, we assume that c 1) log n = 0 for all n > 1 and some ∈ {2, 3}, which implies that −s / ∈ (C Φ H) ⊥ for = 2 or 3. This contradiction implies that c…”
Section: Invariant Subspacesmentioning
confidence: 99%
“…from function theoretic properties of ϕ and vice versa. We refer to monographs by Cowen-MacCluer [4], Shapiro [15] and Zhu [18] for general information of composition operators on the open unit disc D of the complex plane C. Recently, an extensive study of composition operators was carried out on various spaces of Dirichlet series (see [1,2,3,6,12,16]).…”
Section: Introductionmentioning
confidence: 99%
“…Composition operators acting on H (or other spaces of Dirichlet series) have been extensively studied in many papers in recent years (see [1,2,3,5,11,18]). Particularly, the following result comes from [11,18], which characterizes the bounded composition operators on H. And it is convenient to call ϕ a c 0 -symbol if ϕ : C 1/2 → C 1/2 is analytic and satisfies the below conditions such that C ϕ is bounded on H. Theorem A.…”
Section: Introductionmentioning
confidence: 99%