Geodesic
Quasianalytic functional classes in Jordan domains of the complex plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 57-72.

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In this paper, we examine Carleman classes in Jordan domains of the complex plane. We obtain a quasianalyticity criterion for regular Carleman classes, which is universal for all weakly uniform domains. The proof is based on solution of the Dirichlet problem with an unbounded boundary function and a result of Beurling on the estimate of the harmonic measure.
Mots-clés : quasianalytic classes in Jordan domains
Keywords: regular sequences, bilogarithmic quasianalyticity condition, harmonic measure, Dirichlet problem. 
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     author = {R. A. Gaisin},
     title = {Quasianalytic functional classes in {Jordan} domains of the complex plane},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--72},
     publisher = {mathdoc},
     volume = {142},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_142_a4/}
}
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R. A. Gaisin. Quasianalytic functional classes in Jordan domains of the complex plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 57-72. http://geodesic.mathdoc.fr/item/INTO_2017_142_a4/