Geodesic
The Carleman–Goluzin–Krylov formula and analytic functions smooth up to the boundary
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 34-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {The {Carleman{\textendash}Goluzin{\textendash}Krylov} formula and analytic functions smooth up to the boundary},
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V. A. Bart. The Carleman–Goluzin–Krylov formula and analytic functions smooth up to the boundary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 34-70. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a1/

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