Whitney-type extension theorems for jets generated by Sobolev functions

Our approach is based on a representation of the Sobolev space Lpm+1(Rn), p>n, as a union of Cm,(d)(Rn)-spaces where d belongs to a family of metrics on Rn with certain “nice” properties. Here Cm,(d)(Rn) is the space of Cm-functions on Rn whose partial derivatives of order m are Lipschitz functions with respect to d. This enables us to show that, for every non-negative integer m and every p∈(n,∞), the very same classical linear Whitney extension operator as in [31] provides an almost optimal extension of m-jets generated by Lpm+1-functions.