Inner factors of analytic functions of variable smoothness in the closed disc

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Inner factors of analytic functions of variable smoothness in the closed disc. / Shirokov, N. A.

In: St. Petersburg Mathematical Journal, Vol. 32, No. 5, 10.2021, p. 929-954.

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

BibTeX

@article{5a33bf57c14e4a6f87f990f4f2bd7539,

title = "Inner factors of analytic functions of variable smoothness in the closed disc",

abstract = "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).",

keywords = "inner functions, inner-outer Nevanlinna factorization, Lebesgue spaces of variable smoothness",

author = "Shirokov, {N. A.}",

note = "Publisher Copyright: {\textcopyright} 2021. American Mathematical Society.",

year = "2021",

month = oct,

doi = "10.1090/spmj/1678",

language = "English",

volume = "32",

pages = "929--954",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "5",

}

RIS

TY - JOUR

T1 - Inner factors of analytic functions of variable smoothness in the closed disc

AU - Shirokov, N. A.

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: 86249775