Real interpolation of spaces of differential forms (Q663233)

Let \(\Omega\) be a bounded Lipschitz domain and let \(H^s(\Omega,\Lambda^l)\) be the Sobolev space of all \(l\)-differential forms \(\omega=\sum_{i_1<\dots<i_l} \omega_{i_1,\dots,i_l} dx_{i_1}\wedge\dots\wedge dx_{i_l},\) where \(\omega_{i_1,\dots,i_l}\in H^s(\Omega).\) If \(d\) is the exterior derivative, then \[ H^s:=H^s(d,\Omega,\Lambda^l)=\{\omega\in H^s(\Omega,\Lambda^l): d\omega\in H^s(\Omega,\Lambda^{l+1})\}. \] The authors prove the formula \[ (H^{s_0}, H^{s_1})_{\theta,2}=H^s,\; s=(1-\theta)s_0+\theta s_1,\;0<\theta<1, \] where \(( , )_{\theta,2}\) is the \(K\)-interpolation method of Peetre.