Quasianalyticity criterion of Salinas-Korenblyum type for convex domains

The quasianalyticity problem of the class CI(Mn) for interval I is known to be solved by the Denjoy-Carleman theorem. It follows from well-known Men'shov example that not only this theorem but the very statement of the quasianalyticity problem of the class CK(Mn) doesn't expand on the case of arbitrary continuum K of the complex plain. The quasianalyticity problem was studied for Jordan domains and rectifiable arcs including quasismooth arcs by a number of authors. We discuss in this article theorems of Denjoy-Carleman type in the convex domains of the complex plane, more precisely, connection between R. S. Yulmukhametov criterion of quasianalyticity of the Carleman class H(D,Mn) for arbitrary convex domain D and R. Salinas criterion for the class H(Δα,Mn) with angle Δα={z:|argz|≤π2α, 0