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Duality theorems for coinvariant subspaces of H1. / Bessonov, R. V.

In: Advances in Mathematics, Vol. 271, 05.02.2015, p. 62-90.

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

Harvard

Bessonov, RV 2015, 'Duality theorems for coinvariant subspaces of H1', Advances in Mathematics, vol. 271, pp. 62-90. https://doi.org/10.1016/j.aim.2014.11.012

APA

Bessonov, R. V. (2015). Duality theorems for coinvariant subspaces of H1. Advances in Mathematics, 271, 62-90. https://doi.org/10.1016/j.aim.2014.11.012

Vancouver

Bessonov RV. Duality theorems for coinvariant subspaces of H1. Advances in Mathematics. 2015 Feb 5;271:62-90. https://doi.org/10.1016/j.aim.2014.11.012

Author

Bessonov, R. V. / Duality theorems for coinvariant subspaces of H1. In: Advances in Mathematics. 2015 ; Vol. 271. pp. 62-90.

BibTeX

@article{40b9c23a176a4b2c811e6782293c6eb0,
title = "Duality theorems for coinvariant subspaces of H1",
abstract = "Let θ be an inner function satisfying the connected level set condition of B. Cohn, and let Kθ1 be the shift-coinvariant subspace of the Hardy space H1 generated by θ. We describe the dual space to Kθ1 in terms of a bounded mean oscillation with respect to the Clark measure σα of θ. Namely, we prove that (Kθ1∩zH1)*=BMO(σα). The result yields a two-sided estimate for the operator norm of a finite Hankel matrix of size n×n via BMO(μ2n)-norm of its standard symbol, where μ2n is the Haar measure on the group {ξ∈C:ξ2n=1}.",
keywords = "Atomic Hardy space, Bounded mean oscillation, Clark measure, Discrete Hilbert transform, Inner function, Truncated Hankel operators",
author = "Bessonov, {R. V.}",
year = "2015",
month = feb,
day = "5",
doi = "10.1016/j.aim.2014.11.012",
language = "English",
volume = "271",
pages = "62--90",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Duality theorems for coinvariant subspaces of H1

AU - Bessonov, R. V.

PY - 2015/2/5

Y1 - 2015/2/5

N2 - Let θ be an inner function satisfying the connected level set condition of B. Cohn, and let Kθ1 be the shift-coinvariant subspace of the Hardy space H1 generated by θ. We describe the dual space to Kθ1 in terms of a bounded mean oscillation with respect to the Clark measure σα of θ. Namely, we prove that (Kθ1∩zH1)*=BMO(σα). The result yields a two-sided estimate for the operator norm of a finite Hankel matrix of size n×n via BMO(μ2n)-norm of its standard symbol, where μ2n is the Haar measure on the group {ξ∈C:ξ2n=1}.

AB - Let θ be an inner function satisfying the connected level set condition of B. Cohn, and let Kθ1 be the shift-coinvariant subspace of the Hardy space H1 generated by θ. We describe the dual space to Kθ1 in terms of a bounded mean oscillation with respect to the Clark measure σα of θ. Namely, we prove that (Kθ1∩zH1)*=BMO(σα). The result yields a two-sided estimate for the operator norm of a finite Hankel matrix of size n×n via BMO(μ2n)-norm of its standard symbol, where μ2n is the Haar measure on the group {ξ∈C:ξ2n=1}.

KW - Atomic Hardy space

KW - Bounded mean oscillation

KW - Clark measure

KW - Discrete Hilbert transform

KW - Inner function

KW - Truncated Hankel operators

UR - http://www.scopus.com/inward/record.url?scp=84916218337&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.11.012

DO - 10.1016/j.aim.2014.11.012

M3 - Article

AN - SCOPUS:84916218337

VL - 271

SP - 62

EP - 90

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 36321023