Let Cm,1(ℝn) be the space of functions on ℝn whose mth derivatives are Lipschitz 1. For E ⊂ ℝn, let Cm,1(E) be the space of all restrictions to E of functions in Cm,1(ℝn). We show that there exists a bounded linear operator T: Cm,1(E) → C m,1(ℝn) such that, for any f εC m,1(E), we have Tf= f on E.
All Science Journal Classification (ASJC) codes
- Linear operators
- Whitney extension problem