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Composition Operators from the Hardy Space to the Zygmund‐Type Space on the Upper Half‐Plane

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  • Stevo Stević

Abstract

Here we introduce the nth weighted space on the upper half‐plane Π+ = {z ∈ ℂ : Im z > 0} in the complex plane ℂ. For the case n = 2, we call it the Zygmund‐type space, and denote it by 𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator Cφf(z) = f(φ(z)) from the Hardy space Hp(Π+) on the upper half‐plane, to the Zygmund‐type space, where φ is an analytic self‐map of the upper half‐plane.

Suggested Citation

  • Stevo Stević, 2009. "Composition Operators from the Hardy Space to the Zygmund‐Type Space on the Upper Half‐Plane," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:161528
    DOI: 10.1155/2009/161528
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    References listed on IDEAS

    as
    1. Stevo Stević, 2008. "Essential Norms of Weighted Composition Operators from the -Bloch Space to a Weighted-Type Space on the Unit Ball," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-11, November.
    2. Songxiao Li & Stevo Stević, 2007. "Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    3. Stevo Stević, 2007. "On Bloch‐Type Functions with Hadamard Gaps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    4. Songxiao Li & Stevo Stevic, 2007. "Weighted Composition Operators from H ∞ to the Bloch Space on the Polydisc," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-13, June.
    5. Xiaohong Fu & Xiangling Zhu, 2008. "Weighted Composition Operators on Some Weighted Spaces in the Unit Ball," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    6. Xiaohong Fu & Xiangling Zhu, 2008. "Weighted Composition Operators on Some Weighted Spaces in the Unit Ball," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-8, June.
    7. Stevo Stević, 2008. "Essential Norms of Weighted Composition Operators from the α‐Bloch Space to a Weighted‐Type Space on the Unit Ball," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
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    Cited by:

    1. M. Fatehi, 2010. "On the Generalized Hardy Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Stevo Stević, 2010. "Weighted Differentiation Composition Operators from the Mixed‐Norm Space to the nth Weigthed‐Type Space on the Unit Disk," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).

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