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 Eurasian Math. J., 2018, Volume 9, Number 2, Pages 34–43 (Mi emj295)

On the symbol of nonlocal operators associated with a parabolic diffeomorphism

N. R. Izvarina

S.M. Nikol'skii Mathematical Institute, RUDN University, 6 Miklukho-Maklay St, 117198, Moscow, Russian Federation

Abstract: We study the ellipticity of the symbols of operators associated with parabolic diffeomorphisms of spheres and we show, that if for some smoothness exponent of the Sobolev space the symbol of an operator is invertible, then the symbol is invertible for all exponents of Sobolev spaces.

Keywords and phrases: Sobolev spaces, pseudodifferential operators, symbol, ellipticity, parabolic diffeomorphism.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00373_à The present result was supported by RFBR grant 16-01-00373 (topic no. 022004-2-693).

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MSC: 35S05, 47G30, 46E39
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Citation: N. R. Izvarina, “On the symbol of nonlocal operators associated with a parabolic diffeomorphism”, Eurasian Math. J., 9:2 (2018), 34–43

Citation in format AMSBIB
\Bibitem{Izv18} \by N.~R.~Izvarina \paper On the symbol of nonlocal operators associated with a parabolic diffeomorphism \jour Eurasian Math. J. \yr 2018 \vol 9 \issue 2 \pages 34--43 \mathnet{http://mi.mathnet.ru/emj295}