This article is cited in 9 papers

On inequalities with measures of Sobolev type embedding theorems on open sets of the real axis

D. V. Prokhorov, V. D. Stepanov

Computer Centre Far-Eastern Branch of RAS

Abstract: We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.

Keywords: Sobolev space, weighted Lebesgue space, embedding theorem.

UDC: 517.51

Received: 21.11.2001

 English version: Siberian Mathematical Journal, 2002, 43:4, 694–707

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