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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 15–21
DOI: https://doi.org/10.31857/S2686954322600471 (Mi danma311) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Integral estimates of derivatives of rational functions in Hölder domains

A. D. Baranova, I. R. Kayumovb

a St. Petersburg State University, St. Petersburg, Russia
b Kazan Federal University, Kazan, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S2686954322600471
Abstract: Given a bounded rational function of degree $n$ in a Hölder domain in the complex plane, it is shown that the area integral of the modulus of its derivative is bounded by a quantity of order $\sqrt{\log n}$. The obtained inequality improves a classical result of E.P. Dolzhenko (1966), as well as some of our recent results. Examples are constructed illustrating the influence of the length of the boundary on the behavior of area integrals of the moduli of the derivatives of bounded rational functions.
Keywords: rational functions, Hardy space, Hardy–Littlewood inequality, Hölder domain.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 075-15-2021-602
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2021-602.
Presented: S. V. Kislyakov
Received: 19.07.2022
Revised: 07.09.2022
Accepted: 16.09.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3, Pages 416–422
DOI: https://doi.org/10.1134/S1064562422700077
Bibliographic databases:
Document Type: Article
UDC: 517.535, 517.547
Language: Russian
Citation: A. D. Baranov, I. R. Kayumov, “Integral estimates of derivatives of rational functions in Hölder domains”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 15–21; Dokl. Math., 106:3 (2022), 416–422
Citation in format AMSBIB
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\by A.~D.~Baranov, I.~R.~Kayumov
\paper Integral estimates of derivatives of rational functions in H\"older domains
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 507
\pages 15--21
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\crossref{https://doi.org/10.31857/S2686954322600471}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563839}
\elib{https://elibrary.ru/item.asp?id=49991277}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 3
\pages 416--422
\crossref{https://doi.org/10.1134/S1064562422700077}
Linking options:
  • https://www.mathnet.ru/eng/danma311
  • https://www.mathnet.ru/eng/danma/v507/p15
    • This publication is cited in the following 2 articles:
    1. F. G. Avkhadiev, I. R. Kayumov, S. R. Nasyrov, “Extremal problems in geometric function theory”, Russian Math. Surveys, 78:2 (2023), 211–271  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. D. Baranov, I. R. Kayumov, “Estimates for integrals of derivatives of $n$-valent functions and geometric properties of domains”, Sb. Math., 214:12 (2023), 1674–1693  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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