Sonsuz türevlenebilir fonksiyon uzayları için genişletme operatörü

We start with a review of known linear continuous extension operators for thespaces of Whitney functions. The most general approach belongs to Pawlucki andPle´niak. Their operator is continuous provided that the compact set, where thesfunctions are defined, has Markov property. In this work, we examine some modelcompact sets having no Markov property, but where a linear continuous exten-sion operator exists for the space of Whitney functions given on these sets. Usinglocal interpolation of Whitney functions we can generalize the Pawlucki-Ple´niaksextension operator. We also give an upper bound for the Green function of do-mains complementary to generalized Cantor-type sets, where the Green functiondoes not have the Hülder continuity property. And, for spaces of Whitney func-otions given on multidimensional Cantor-type sets, we give the conditions for theexistence and non-existence of a linear continuous extension operator.Keywords: Extension operator, Green function, Markov inequality, infinitely dif-ferentiable functions, polynomial interpolation.iv