Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces

Let $\mathrm{\Omega }\subseteq {\mathcal{R}}^2$ be a domain, let $X$ be a rearrangement invariant space and let $f\in W^{1}X(\mathrm{\Omega },{\mathcal{R}}^2)$ be a homeomorphism between $\mathrm{\Omega }$ and $f(\mathrm{\Omega })$. Then there exists a sequence of diffeomorphisms $f_k$ converging to $f$ in the space $W^{1}X(\mathrm{\Omega },{\mathcal{R}}^2)$.