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INNER FACTORS OF ANALYTIC FUNCTIONS OF VARIABLE SMOOTHNESS IN THE CLOSED DISK. / Shirokov, N. A.
в: St. Petersburg Mathematical Journal, Том 32, № 5, 10.2021, стр. 929-954.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - INNER FACTORS OF ANALYTIC FUNCTIONS OF VARIABLE SMOOTHNESS IN THE CLOSED DISK
AU - Shirokov, N. A.
N1 - Publisher Copyright: © 2021. American Mathematical Society.
PY - 2021/10
Y1 - 2021/10
N2 - Let p(ϛ) be a positive function defined on the unit circle (Formula presented) and satisfying the condition (Formula presented) (Formula presented). Futhermore, let 0 <α< 1, r ≥ 0, (Formula presented), and assume that (Formula presented). Define a class of analytic functions in the unit disk (Formula presented) as follows: (Formula presented). The following main results are proved. Theorem 1. Let (Formula presented), and let I be an inner function, f/I ∈ H1. Then (Formula presented). Theorem 2. Let (Formula presented), and let I be an inner function, f/I ∈∞. Assume that the multiplicity of every zero of f in (Formula presented) is at least r + 1.Then (Formula presented).
AB - Let p(ϛ) be a positive function defined on the unit circle (Formula presented) and satisfying the condition (Formula presented) (Formula presented). Futhermore, let 0 <α< 1, r ≥ 0, (Formula presented), and assume that (Formula presented). Define a class of analytic functions in the unit disk (Formula presented) as follows: (Formula presented). The following main results are proved. Theorem 1. Let (Formula presented), and let I be an inner function, f/I ∈ H1. Then (Formula presented). Theorem 2. Let (Formula presented), and let I be an inner function, f/I ∈∞. Assume that the multiplicity of every zero of f in (Formula presented) is at least r + 1.Then (Formula presented).
KW - inner functions
KW - inner-outer Nevanlinna factorization
KW - Lebesgue spaces of variable smoothness
UR - http://www.scopus.com/inward/record.url?scp=85114262954&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/b9d47815-f087-3c7e-8302-450a2c53ae2b/
U2 - 10.1090/spmj/1678
DO - 10.1090/spmj/1678
M3 - Article
AN - SCOPUS:85114262954
VL - 32
SP - 929
EP - 954
JO - St. Petersburg Mathematical Journal
JF - St. Petersburg Mathematical Journal
SN - 1061-0022
IS - 5
ER -
ID: 86660021