On the problem of characterizing multipliers for the drury-arveson space

Quanlei Fang; Jingbo Xia

doi:10.1512/iumj.2015.64.5506

On the problem of characterizing multipliers for the drury-arveson space

Quanlei Fang
, Jingbo Xia

Mathematics

University at Buffalo

City University of New York

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

8 Scopus citations

Abstract

Let H²_n be the Drury-Arveson space on the unit ball B in Cn, and suppose that n ≥ 2. Let k_z, z B be the normalized reproducing kernel for H²_n. In this paper, we consider the following rather basic question in the theory of the Drury-Arveson space: for f H²_n, does the condition sup|z |<1 kf kzk imply that f is a multiplier of H²_n We show that the answer is negative. We further show that the analogue of the familiar norm inequality BMO for Hankel operators fails in the Drury-Arveson space.

Original language	English
Pages (from-to)	663-696
Number of pages	34
Journal	Indiana University Mathematics Journal
Volume	64
Issue number	3
DOIs	https://doi.org/10.1512/iumj.2015.64.5506
State	Published - 2015

Keywords

Drury-Arveson space
Multiplier
Reproducing kernel

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10.1512/iumj.2015.64.5506

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abstract = "Let H2n be the Drury-Arveson space on the unit ball B in Cn, and suppose that n ≥ 2. Let kz, z B be the normalized reproducing kernel for H2n. In this paper, we consider the following rather basic question in the theory of the Drury-Arveson space: for f H2n, does the condition sup|z |<1 kf kzk imply that f is a multiplier of H2n We show that the answer is negative. We further show that the analogue of the familiar norm inequality BMO for Hankel operators fails in the Drury-Arveson space.",

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AU - Xia, Jingbo

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AB - Let H2n be the Drury-Arveson space on the unit ball B in Cn, and suppose that n ≥ 2. Let kz, z B be the normalized reproducing kernel for H2n. In this paper, we consider the following rather basic question in the theory of the Drury-Arveson space: for f H2n, does the condition sup|z |<1 kf kzk imply that f is a multiplier of H2n We show that the answer is negative. We further show that the analogue of the familiar norm inequality BMO for Hankel operators fails in the Drury-Arveson space.

KW - Drury-Arveson space

KW - Multiplier

KW - Reproducing kernel

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JF - Indiana University Mathematics Journal

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ER -

On the problem of characterizing multipliers for the drury-arveson space

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