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Compactness of Composition Operators from the Bloch Space ℬ to Q K Spaces

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Abstract

Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator C φ from the Bloch space ℬ into the spaces Q K defined by a nonnegative, nondecreasing function K(r) for 0 ≤ r < ∞. Our compactness condition depends only on ϕ which can be considered as a slight improvement of the known results. The compactness of C ϕ from the Dirichlet space \({\fancyscript D}\) into the spaces Q K is also investigated.

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou 515063, P. R. China

    Hasi Wulan

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  1. Hasi Wulan
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Correspondence to Hasi Wulan.

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This research is supported in part by the National Natural Science Foundation of China (No. 10371069) and the NSF of Guangdong Province of China (No. 04011000)

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Wulan, H. Compactness of Composition Operators from the Bloch Space ℬ to Q K Spaces. Acta Math Sinica 21, 1415–1424 (2005). https://doi.org/10.1007/s10114-005-0584-7

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