On rearrangement invariant hull of generalized Sobolev spaces

In this paper, an equivalent description of the cone of decreasing rearrangements for functions from the Sobolev space ẆE m(Ω), where m ∈ N, Ω is an open bounded domain in Rn, and E = E(Ω) is a rearrangement invariant space is given. It is used to describe the rearrangement invariant hull of the Sobolev space, i.e., the minimal invariant rearrangement space in which the Sobolev space is embedded. Copyright © 2005 by Pleiades Publishing, Inc.