Abstract
Imbedding theorems are proved for abstract anisotropic spaces of Sobolev type. In particular, it is proved that if G is a bounded set satisfying thel horn condition, then there holds the imbedding
where\(\left| {\alpha :l} \right| = \frac{{\alpha _1 }}{{l_1 }} + ... + \frac{{\alpha _n }}{{l_n }} \leqslant 1\), H is a Hilbert space, and A is a self-adjoint positive operator.
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Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 297–301, August, 1977.
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Yakubov, S.Y., Shakhmurov, V.B. Theorems on imbedding in anisotropic spaces of vector-valued functions. Mathematical Notes of the Academy of Sciences of the USSR 22, 657–659 (1977). https://doi.org/10.1007/BF01780977
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DOI: https://doi.org/10.1007/BF01780977