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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 303, Pages 34–70 (Mi znsl896)  
The Carleman–Goluzin–Krylov formula and analytic functions smooth up to the boundary

V. A. Bart

Cardiology Institute named after V. A. Almazov
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Abstract: The classical Carleman–Goluzin–Krylov formula recovers an $H^1$-function from its boundary values on an arc. We study this formula when it is applied to Lipschitz spaces of order $\alpha\le1$ and to higher order smoothness spaces. The rate of convergence is estimated and some (counter-) examples are given.
Received: 10.07.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 129, Issue 4, Pages 3944–3965
DOI: https://doi.org/10.1007/s10958-005-0331-8
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. A. Bart, “The Carleman–Goluzin–Krylov formula and analytic functions smooth up to the boundary”, Investigations on linear operators and function theory. Part 31, Zap. Nauchn. Sem. POMI, 303, POMI, St. Petersburg, 2003, 34–70; J. Math. Sci. (N. Y.), 129:4 (2005), 3944–3965
Citation in format AMSBIB
\Bibitem{Bar03}
\by V.~A.~Bart
\paper The Carleman--Goluzin--Krylov formula and analytic functions smooth up to the boundary
\inbook Investigations on linear operators and function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 303
\pages 34--70
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl896}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2037530}
\zmath{https://zbmath.org/?q=an:1153.30033}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 4
\pages 3944--3965
\crossref{https://doi.org/10.1007/s10958-005-0331-8}
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