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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 447, Pages 75–89 (Mi znsl6295)  
Comparison of boundary smoothness for an analytic function and for its modulus in the case of the upper half-plane

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
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Abstract: The results of a recent paper by A. V. Vasin, S. V. Kislyakov, and the author are extended to the case of outer functions in the upper half-plane. As in the case of the disk, it can only be guaranteed that the smoothness of an outer function is at least one half as high as that of it modulus, but the quantitative manifestation of this effect is different – in particular, it depends on the position of the point at which smoothness is measured.
Key words and phrases: outer function, Holder type conditions, Poisson measure, logarithmic integral, mean oscillation, Hilbert transform.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00198-A
Received: 10.10.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 229, Issue 5, Pages 534–544
DOI: https://doi.org/10.1007/s10958-018-3696-1
Bibliographic databases:
Document Type: Article
UDC: 517.547.3
Language: Russian
Citation: A. N. Medvedev, “Comparison of boundary smoothness for an analytic function and for its modulus in the case of the upper half-plane”, Investigations on linear operators and function theory. Part 44, Zap. Nauchn. Sem. POMI, 447, POMI, St. Petersburg, 2016, 75–89; J. Math. Sci. (N. Y.), 229:5 (2018), 534–544
Citation in format AMSBIB
\Bibitem{Med16}
\by A.~N.~Medvedev
\paper Comparison of boundary smoothness for an analytic function and for its modulus in the case of the upper half-plane
\inbook Investigations on linear operators and function theory. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 447
\pages 75--89
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6295}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3580163}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 5
\pages 534--544
\crossref{https://doi.org/10.1007/s10958-018-3696-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85041495402}
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