On the rearrangement-invariant hull of generalized Sobolev spaces

From the text (translated from the Russian): "We establish an equivalent description of the cone of decreasing permutations for functions belonging to the Sobolev space dot W^m_E(Omega), where min bf N, Omega is a bounded open domain in {bf R}^n, and E=E(Omega) is a rearrangement-invariant space. Based on it, we give a description of the rearrangement-invariant hull of the Sobolev space, i.e., the minimal rearrangement-invariant space into which the Sobolev space is embedded."