Research output: Contribution to journal › Article › peer-review
Majorants of meromorphic functions with fixed poles. / Baranov, A. D.; Borichev, A. A.; Havin, V. P.
In: Indiana University Mathematics Journal, Vol. 56, No. 4, 30.10.2007, p. 1595-1628.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Majorants of meromorphic functions with fixed poles
AU - Baranov, A. D.
AU - Borichev, A. A.
AU - Havin, V. P.
PY - 2007/10/30
Y1 - 2007/10/30
N2 - Let B be a meromorphic Blaschke product in the upper half-plane with zeros Zn and let KB - H2 ⊖ BH2 be the associated model subspace of the Hardy space H2. A nonnegative function w on the real line is said to be an admissible majorant for K B if there is a non-zero function f ∈ KB such that |f| ≤ w a.e. on ℝ. We study the relations between the distribution of the zeros of a Blaschke product B and the class of admissible majorants for the space KB.
AB - Let B be a meromorphic Blaschke product in the upper half-plane with zeros Zn and let KB - H2 ⊖ BH2 be the associated model subspace of the Hardy space H2. A nonnegative function w on the real line is said to be an admissible majorant for K B if there is a non-zero function f ∈ KB such that |f| ≤ w a.e. on ℝ. We study the relations between the distribution of the zeros of a Blaschke product B and the class of admissible majorants for the space KB.
KW - Admissible majorant
KW - Blaschke product
KW - Entire function
KW - Hardy space
KW - Hilbert transform
KW - Meromorphic function
KW - Model subspace
UR - http://www.scopus.com/inward/record.url?scp=35448956130&partnerID=8YFLogxK
U2 - 10.1512/iumj.2007.56.3045
DO - 10.1512/iumj.2007.56.3045
M3 - Article
AN - SCOPUS:35448956130
VL - 56
SP - 1595
EP - 1628
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 4
ER -
ID: 32722185