A simple proof of the $p$-adic version of the Sobolev embedding theorem

Yong-Cheol Kim

doi:10.4134/CKMS.2010.25.1.27

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Commun. Korean Math. Soc. 2010; 25(1): 27-36

Printed March 1, 2010

https://doi.org/10.4134/CKMS.2010.25.1.27

A simple proof of the $p$-adic version of the Sobolev embedding theorem

Yong-Cheol Kim

Korea University

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Abstract

We give a simple proof of certain mapping properties of the $p$-adic Riesz potential and Bessel potential, and the $p$-adic version of the Sobolev embedding theorem obtained in [6].

Keywords: $p$-adic vector space, the $p$-adic Riesz and Bessel potential, Sobolev embedding theorem

MSC numbers: 11S80, 11K70, 11E95

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Communications of the
Korean Mathematical Society CKMS

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A simple proof of the $p$-adic version of the Sobolev embedding theorem

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A simple proof of the $p$-adic version of the Sobolev embedding theorem

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