Let C m,ω (R n ) be the space of functions on R n whose m th derivatives have modulus of continuity ω. For E ⊂ R n , let C m,ω (E) be the space of all restrictions to E of functions in C m,ω (R n ). We show that there exists a bounded linear operator T : C m,ω (E) → C m,ω (R n ) such that, for any f ∈ C m,ω (E), we have Tf = f on E.