Geodesic
On a condition necessary for interpolation by functions in the Lipschitz class
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 39-42 
A. V. Vasin. On a condition necessary for interpolation by functions in the Lipschitz class. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 39-42. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a1/
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     title = {On a~condition necessary for interpolation by functions in the {Lipschitz} class},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For the weak modulus of continuity and the corresponding Lipschitz class, a necessary condition for interpolation by analytic functions is given in the form of Dyn'kin's inequality.

[1] E. M. Dynkin, “Mnozhestva svobodnoi interpolyatsii dlya klassov Geldera”, Mat. sbornik, 109(151):1(5) (1979), 107–128 | MR

[2] A. M. Kotochigov, “Interpolyatsiya analiticheskimi funktsiyami, gladkimi vplot do granitsy”, Zap. nauchn. semin. LOMI, 30, 1972, 167–169 | Zbl

[3] Dzh. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR