See 

<cite authors="Jonsson, A.; Wallin, Hans">_Jonsson, A.; Wallin, Hans_, [**A Whitney extension theorem in \(L^p\) and Besov spaces**](http://dx.doi.org/10.5802/aif.684), Ann. Inst. Fourier 28, No. 1, 139-192 (1978). [ZBL0369.46031](https://zbmath.org/?q=an:0369.46031).</cite>

Proposition 7.3 is exactly what you are looking for (and a bit more).