Local growth envelopes and optimal embeddings of generalized Sobolev spaces. (English. Russian original) Zbl 1142.46016
Dokl. Math. 74, No. 2, 692-695 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 410, No. 4, 445-448 (2006).
Summary: Order-sharp estimates for the local growth envelopes of functions from the generalized Sobolev spaces are obtained and the rearrangement-invariant hulls of the generalized Lorentz-Sobolev spaces (that is, the minimal rearrangement-invariant spaces in which the generalized Lorentz-Sobolev spaces are embedded) are explicitly described.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
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