For m-th order gradients, Sobolev embeddings between rearrangement-invariant spaces are characterized by a one-dimensional Hardy inequality, with optimal target and domain spaces identified, including in Orlicz spaces.
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Embeddings of homogeneous Sobolev spaces on the entire space
For m-th order gradients, Sobolev embeddings between rearrangement-invariant spaces are characterized by a one-dimensional Hardy inequality, with optimal target and domain spaces identified, including in Orlicz spaces.