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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1969 Volume 6, Issue 2, Pages 129–138 (Mi mzm6916)

This article is cited in 7 papers

An embedding theorem for a limiting exponent

O. V. Besova, V. P. Il'inb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences

Abstract: We consider the function space $B_{p,\theta}^l(\Omega)$ of functions $f(x)$, defined on the domain $\Omega$ of a certain class and characterized by specific differential-difference properties in $L_p(\Omega)$. We prove a theorem on the embedding $B_{p,q}^l\subset\Omega)$ in the case when $l=n/p-n/q>0$ and its generalization for vector $l$, $p$, $q$.

UDC: 517.5

Received: 11.11.1968


 English version:
Mathematical Notes, 1969, 6:2, 537–542

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