RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2015, Volume 434, Pages 101–115 (Mi znsl6145)  

This article is cited in 2 scientific papers (total in 2 papers)

Drop of the smoothness of an outer function compared to the smoothness of its modulus, under restrictions on the size of boundary values

A. N. Medvedevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg Electrotechnical University, St. Petersburg, Russia

Abstract: Let $F$ be an outer function on the unit disk. It is well known that its smootheness properties may be two times worse that those of the modulus of its boundary values, but under some restrictions on $\log|F|$ this gap becomes smaller. It is shown that the smoothness decay admits a convenient description in terms of a rearrangement invariant Banach function space containing $\log|F|$. All results are of pointwise nature.

Key words and phrases: outer function, harmonic conjugation operator, symmetric space, nonincreasing rearrengement, mean oscillation.

Full text: PDF file (236 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2016, 215:5, 608–616

Bibliographic databases:

UDC: 517
Received: 31.08.2015

Citation: A. N. Medvedev, “Drop of the smoothness of an outer function compared to the smoothness of its modulus, under restrictions on the size of boundary values”, Investigations on linear operators and function theory. Part 43, Zap. Nauchn. Sem. POMI, 434, POMI, St. Petersburg, 2015, 101–115; J. Math. Sci. (N. Y.), 215:5 (2016), 608–616

Citation in format AMSBIB
\Bibitem{Med15}
\by A.~N.~Medvedev
\paper Drop of the smoothness of an outer function compared to the smoothness of its modulus, under restrictions on the size of boundary values
\inbook Investigations on linear operators and function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 434
\pages 101--115
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6145}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493703}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 5
\pages 608--616
\crossref{https://doi.org/10.1007/s10958-016-2867-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84965079398}


Linking options:
  • http://mi.mathnet.ru/eng/znsl6145
  • http://mi.mathnet.ru/eng/znsl/v434/p101

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Medvedev, “Comparison of boundary smoothness for an analytic function and for its modulus in the case of the upper half-plane”, J. Math. Sci. (N. Y.), 229:5 (2018), 534–544  mathnet  crossref  mathscinet
    2. A. N. Medvedev, “Obschie gëlderovy usloviya poryadka ne vyshe 2 dlya analiticheskoi funktsii i ee modulya v granichnoi tochke”, Issledovaniya po lineinym operatoram i teorii funktsii. 45, Zap. nauchn. sem. POMI, 456, POMI, SPb., 2017, 155–159  mathnet
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:196
    Full text:60
    References:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020