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Bounded projections and duality on spaces of holomorphic functions in the unit ball ofℂ n

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Abstract

In this paper three Banach spacesA 0(ϕ),A ∞ andA 1(ϕ) of functions holomorphic in the unit ballB ofℂ n are defined. We exhibit bounded projections fromC 0(B) ontoA 0(ϕ), fromL 1(B) ontoA 1(ϕ), and fromL∞(B) ontoA∞(ϕ). Using these projections, we show thatA 0(ϕ)* ≅A 1(ϕ) andA 1(ϕ)* ≅A∞(ϕ).

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Authors and Affiliations

  1. Department of Mathematics, Fudan University, 200433, Shanghai, People's Republic of China

    Ren Fuyao

  2. Department of Mathematics, Hunan Normal University, 410081, Changsha, People's Republic of China

    Xiao Jianbin

Authors
  1. Ren Fuyao
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  2. Xiao Jianbin
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Supported in part by the National Natural Science Foundation of China.

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Fuyao, R., Jianbin, X. Bounded projections and duality on spaces of holomorphic functions in the unit ball ofℂ n . Acta Mathematica Sinica 11, 29–36 (1995). https://doi.org/10.1007/BF02274044

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  • DOI: https://doi.org/10.1007/BF02274044

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