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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, Volume 15, Issue 3, Pages 61–68
(Mi vngu376)
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Change of variables operators in weighted Sobolev spaces on Carnot groups
N. A. Evseev Novosibirsk State University
Abstract:
We study mappings inducing a bounded composition operator on weighted Sobolev spaces on Carnot groups. An analytical description of these mappings is given in terms of integrability of weighted distortion function. For the special cases we prove that mapping which generates a bounded composition operator is partially absolutely continuous on almost all horizontal lines.
Keywords:
composition operators, weighted Sobolev spaces on Carnot groups.
DOI:
https://doi.org/10.17377/PAM.2015.15.305
Full text:
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English version:
Journal of Mathematical Sciences, 2017, 221:6, 826–832
UDC:
517.518.23 Received: 10.09.2015
Citation:
N. A. Evseev, “Change of variables operators in weighted Sobolev spaces on Carnot groups”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 61–68; J. Math. Sci., 221:6 (2017), 826–832
Citation in format AMSBIB
\Bibitem{Evs15}
\by N.~A.~Evseev
\paper Change of variables operators in weighted Sobolev spaces on Carnot groups
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 3
\pages 61--68
\mathnet{http://mi.mathnet.ru/vngu376}
\crossref{https://doi.org/10.17377/PAM.2015.15.305}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 221
\issue 6
\pages 826--832
\crossref{https://doi.org/10.1007/s10958-017-3270-2}
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