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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2003_303_a1,
     author = {V. A. Bart},
     title = {The {Carleman--Goluzin--Krylov} formula and analytic functions smooth up to the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {34--70},
     publisher = {mathdoc},
     volume = {303},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a1/}
}
TY  - JOUR
AU  - V. A. Bart
TI  - The Carleman--Goluzin--Krylov formula and analytic functions smooth up to the boundary
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 34
EP  - 70
VL  - 303
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a1/
LA  - ru
ID  - ZNSL_2003_303_a1
ER  - 
%0 Journal Article
%A V. A. Bart
%T The Carleman--Goluzin--Krylov formula and analytic functions smooth up to the boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 34-70
%V 303
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a1/
%G ru
%F ZNSL_2003_303_a1
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/