Siberian Federal University

We describe the strong dual space (Os(D)) for the space Os(D) = Hs(D) \ O(D) of holo- morphic functions from the Sobolev space Hs(D), s 2 Z, over a bounded simply connected plane domain D with infinitely differential boundary @D. We identify the dual space with the space of holomorhic functions on Cn nD that belong to H1�����s(GnD) for any bounded domain G, containing the compact D, and vanish at the infinity. As a corollary, we obtain a description of the strong dual space (OF (D)) for the space OF (D) of holomorphic functions of finite order of growth in D (here, OF (D) is endowed with the inductive limit topology with respect to the family of spaces Os(D), s 2 Z). In this way we extend the classical Grothendieck–K¨othe–Sebasti˜ao e Silva duality for the space of holomorphic functions