Acta mathematica scientia, Series B >
COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL
Received date: 2006-09-10
Revised date: 2007-08-07
Online published: 2009-09-20
Supported by
Supported by NSF of China (10571164) and SRFDP of Higher Education (20050358052)
Let φ be a holomorphic self-map of Bn and Ψ ∈ H(Bn). A composition type operator is defined by TΨ, φ(f)= Ψf ο φ for f ∈ H(Bn), 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 TΨ, φ to be bounded or compact from Hardy space Hp(Bn) to μ-Bloch space B(Bn). 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
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 . DOI: 10.1016/S0252-9602(09)60115-6
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