О ПЕРЕСТАНОВОЧНО-ИНВАРИАНТНОЙ ОБОЛОЧКЕ ОБОБЩЕННЫХ ПРОСТРАНСТВ СОБОЛЕВА

On rearrangement-invariant hull of generalized Sobolev spaces

The equivalent description of decreasing rearrangement cone is established for the function from Sobolev space W(dot)m E(Ω), where m∈N, Ω - a bounded open domain in Rn, E=E(Ω) - rearrangement-invariant space. On its base the description of rearrangement-invariant hull of Sobolev space is given, that is the minimal rearrangement-invariant space in which the Sobolev space is embedded.