Nonclassical interpolation in spaces of analytic functions smooth up to the boundary

One considers the following problem. Let X be the space of smooth functions on the circumference and let Y be the space of functions analytic in the disk and smooth up to the boundary. One has to find necessary and sufficient conditions on the closed subset E of the circumference that ensure the inclusion^X¦_E^y¦_E. The problem is solved in the case when the space X is a Carleman class and Y is either an analytic Carleman class having weaker smoothness properties than X, or a Hölder class A^s with arbitrary exponent s.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 7–26, 1982.