A closer look at a Poisson-like condition on the drury-Arveson space

Quanlei Fang; Jingbo Xia

doi:10.1090/proc/14923

A closer look at a Poisson-like condition on the drury-Arveson space

Quanlei Fang
, Jingbo Xia

Mathematics

City University of New York

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

2 Scopus citations

Abstract

Let M be the collection of the multipliers of the Drury-Arveson space H_n ² , n ≥ 2. In a recent paper [Adv. Math. 335 (2018), pp. 372-404], Aleman et al. showed that for f ∈ H_n ² , the condition sup_|z|<₁ Re〈f, K_zf〉 < ∞ is sufficient for the membership f ∈ M. We show that this condition is not necessary for f ∈ M. Moreover, we show that the condition sup_|z|<₁ Re〈f, K_zf〉 < ∞ only captures a nowhere dense subset of M.

Original language	English
Pages (from-to)	2497-2507
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	6
DOIs	https://doi.org/10.1090/proc/14923
State	Published - 2020

Keywords

Drury-Arveson space
Multiplier

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10.1090/proc/14923

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abstract = "Let M be the collection of the multipliers of the Drury-Arveson space Hn 2 , n ≥ 2. In a recent paper [Adv. Math. 335 (2018), pp. 372-404], Aleman et al. showed that for f ∈ Hn 2 , the condition sup|z|<1 Re〈f, Kzf〉 < ∞ is sufficient for the membership f ∈ M. We show that this condition is not necessary for f ∈ M. Moreover, we show that the condition sup|z|<1 Re〈f, Kzf〉 < ∞ only captures a nowhere dense subset of M.",

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AU - Xia, Jingbo

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KW - Drury-Arveson space

KW - Multiplier

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A closer look at a Poisson-like condition on the drury-Arveson space

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