Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 837-849

SOBOLEV SPACES ON METRIZABLE GROUPS

Przemyslaw Górka and Tomasz Kostrzewa

Warsaw University of Technology, Department of Mathematics and Information Sciences
Ul. Koszykowa 75, 00-662 Warsaw, Poland; pgorka 'at' mini.pw.edu.pl

Warsaw University of Technology, Department of Mathematics and Information Sciences
Ul. Koszykowa 75, 00-662 Warsaw, Poland; kostrzewat 'at' mini.pw.edu.pl

Abstract. We continue our research on Sobolev spaces on locally compact abelian groups. In this paper, we focus on embedding results when the dual group is metrizable. We show the density of continuous functions. As a by-product we obtain new embeddings of Sobolev spaces defined over p-adic numbers.

2010 Mathematics Subject Classification: Primary 32A99, 46E35, 22B99.

Key words: Abstract harmonic analysis, Sobolev spaces, analysis on metric measure spaces, p-adic analysis, embeddings, Moser-Trudinger inequality.

Reference to this article: P. Górka and T. Kostrzewa: Sobolev spaces on metrizable groups. Ann. Acad. Sci. Fenn. Math. 40 (2015), 837-849.

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doi:10.5186/aasfm.2015.4045