COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

doi:10.1016/S0252-9602(09)60115-6

Abstract

Abstract:

Let φ be a holomorphic self-map of B_n and Ψ ∈ H(B_n). A composition type operator is defined by T_Ψ, φ(f)= Ψf ο φ for f ∈ H(B_n), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator T_Ψ_, φ to be bounded or compact from Hardy space H_p(B_n) to μ-Bloch space B(B_n). The conditions are some supremums concerned with Ψ, φ, their derivatives and Bergman metric of $\Bn$. At the same time, two corollaries are obtained.

Key words: Hardy spaces, μBloch spaces, composition type operators, boundedness, compactness

CLC Number:

47B33

WANG Xiong-Liang, LIU Ta-Shun. COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL[J].Acta mathematica scientia,Series B, 2009, 29(5): 1430-1438.

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References

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COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

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