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