On embeddings of grand grand Sobolev-Morrey spaces with dominant mixed derivatives. (English) Zbl 1453.46022

Summary: In this paper it is constructed a new grand grand Sobolev-Morrey \(S_{p),\varkappa),a,\alpha}^lW(G)\) spaces with dominant mixed derivatives. With help integral representation of generalized mixed derivatives of functions, defined on \(n\)-dimensional domains satisfying flexible horn condition, an embedding theorem is proved. In other works, the embedding theorem is proved in these spaces and belonging of the generalized mixed derivatives of functions from these spaces to the Hölder class, was studied.


46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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