An approximation theorem in Musielak-Orlicz-Sobolev spaces

In this paper we prove the uniform boundedness of the operators of convolution in the Musielak-Orlicz spaces and the density of $C_0^{\mathrm{\infty }}({\mathbb{R}}^n)$ in the Musielak-Orlicz-Sobolev spaces by assuming a condition of Log-Hölder type of continuity.