## 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.

Full Text (PDF) [143 KB]

### Key words

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

### AMS subject classifications

41A10, 46E35, 46G10

< Back