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hh=\ Rn\^)\eiw^d$ 0. The space 2)^(0) equipped with the inductive limit topology, as 2){Q), is Frechet and we call ^{Q), the dual of WJ^Q), the Beurling's generalized distributionspace. They denote by GJ^Q) the set of all complex valued functions ^.S)S.Q') for all IUfor every X>0 and every (Q) which have compact support contained in Q. They also extend the Schwartz space denoting by Sw the space of all C°°-function (j>in L\Rn) with the property that for each multi-index a and each non-negative number A

Sobolev spaces in the generalized distribution spaces of Beurling type