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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
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