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Tr. Mat. Inst. Steklova, 2004, Volume 245, Pages 114–124 (Mi tm178)  

Analysis Based on the Dirichlet Space Theory on Some Extensions of $\mathbb Q_p$

H. Kaneko

Tokyo University of Science

Abstract: The space $\mathcal F_{r,p}$, which was designed so as to play a role similar to the ordinary Sobolev space $W_{r,p}$, is introduced as a cornerstone for analyzing nonlinear potential theoretic features of the state space with a measure-symmetric semigroup. The aim of this article is to reveal a sufficient condition for the coincidence of the counterparts of the Sobolev space and to derive the equivalence of the norms associated with those counterparts.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 105–116

Bibliographic databases:

UDC: 517.94+512.625
Received in October 2003
Language: English

Citation: H. Kaneko, “Analysis Based on the Dirichlet Space Theory on Some Extensions of $\mathbb Q_p$”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 245, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 114–124; Proc. Steklov Inst. Math., 245 (2004), 105–116

Citation in format AMSBIB
\Bibitem{Kan04}
\by H.~Kaneko
\paper Analysis Based on the Dirichlet Space Theory on Some Extensions of~$\mathbb Q_p$
\inbook Selected topics of $p$-adic mathematical physics and analysis
\bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 245
\pages 114--124
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm178}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099875}
\zmath{https://zbmath.org/?q=an:1098.60077}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 245
\pages 105--116


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