Geodesic
Free interpolation of bounded harmonic functions by analytic ones
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 209-212 
V. A. Tolokonnikov. Free interpolation of bounded harmonic functions by analytic ones. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 209-212. http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a16/
@article{ZNSL_1982_107_a16,
     author = {V. A. Tolokonnikov},
     title = {Free interpolation of bounded harmonic functions by analytic ones},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {209--212},
     year = {1982},
     volume = {107},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a16/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $L^p$ (resp. $H^p$) denote the space of harmonic (analytic) functions in the unit disk $\mathbb D$ with the norm $\|f\|_p=\lim_{r\to1-2}(\int_{\mathbb T}|f(re^{it}|^p\,dt)^{1/p}$, $1\le p\le\infty$. A complete characterization of subsets $E$, $E\subset\mathbb D$, satisfying $L^\infty|_E=H^\infty|_E$ is given. There are some results about sets $E$, $E\subset\mathbb D$ with $L^p|_E=H^p|_E$, $1\le p<\infty$.