S. K. Vodop'yanov, A. D.-O. Ukhlov, “Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. II”, Mat. Tr., 2004, Volume 7, Number 1,Pages <nobr>13

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Set Functions and Their Applications in the Theory of Lebesgue and Sobolev Spaces. II

S. K. Vodop'yanov^a, A. D.-O. Ukhlov^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Khabarovsk State University of Technology

Abstract: We study the properties of the mappings inducing a bounded operator of Lebesgue or Sobolev spaces by change of variable and the properties of the operator of extension of functions in Sobolev classes beyond the domain of definition.

Key words: quasiadditive set function, Lebesgue space, Sobolev space, embedding theorems.

UDC: 517.518.1+517.54

Received: 02.04.2002