Weierstrass' theorem in weighted Sobolev spaces with $k$ derivatives: announcement of results

Ana Portilla, Yamilet Quintana, José M. Rodríguez, and Eva Tourís

Abstract

We characterize the set of functions which can be approximated by smooth functions and by polynomials with the norm $$\|f\|_{W^{k,\infty}(w)}:=\sum_{j=0}^k \|f^{(j)}\|_{L^{\infty}(w_j)},$$ for a wide range of (even non-bounded) weights $w_j$'s. We allow a great deal of independence among the weights $w_j$'s.

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Key words

Weierstrass' theorem, weight, Sobolev spaces, weighted Sobolev spaces

AMS subject classifications

41A10, 46E35, 46G10

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