Characterisations of Bloch functions in the unit ball of ℂ n, I

Zengjian Lou; Hasi Wulan

doi:10.1017/s000497270003759x

Characterisations of Bloch functions in the unit ball of ℂ ⁿ, I

Zengjian Lou^*, Hasi Wulan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Weighted Hadamard product characterisations of Bloch functions in the unit ball of ℂⁿ are studied. In particular, we prove that f belongs to the Bloch space B(B_n) if and only if the non-weighted Hadamard products of f and g belong to BMOA(Uⁿ) for all f in G ₀¹(B_n), a subspace of the Hardy space H ¹(B_n).

Original language	English
Pages (from-to)	205-212
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	68
Issue number	2
DOIs	https://doi.org/10.1017/s000497270003759x
Publication status	Published - Oct 2003

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title = "Characterisations of Bloch functions in the unit ball of ℂ n, I",

abstract = "Weighted Hadamard product characterisations of Bloch functions in the unit ball of ℂn are studied. In particular, we prove that f belongs to the Bloch space B(Bn) if and only if the non-weighted Hadamard products of f and g belong to BMOA(Un) for all f in G 01(Bn), a subspace of the Hardy space H 1(Bn).",

author = "Zengjian Lou and Hasi Wulan",

year = "2003",

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doi = "10.1017/s000497270003759x",

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AU - Lou, Zengjian

AU - Wulan, Hasi

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N2 - Weighted Hadamard product characterisations of Bloch functions in the unit ball of ℂn are studied. In particular, we prove that f belongs to the Bloch space B(Bn) if and only if the non-weighted Hadamard products of f and g belong to BMOA(Un) for all f in G 01(Bn), a subspace of the Hardy space H 1(Bn).

AB - Weighted Hadamard product characterisations of Bloch functions in the unit ball of ℂn are studied. In particular, we prove that f belongs to the Bloch space B(Bn) if and only if the non-weighted Hadamard products of f and g belong to BMOA(Un) for all f in G 01(Bn), a subspace of the Hardy space H 1(Bn).

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DO - 10.1017/s000497270003759x

M3 - Article

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SP - 205

EP - 212

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

Characterisations of Bloch functions in the unit ball of ℂ ⁿ, I

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