A second look of Sobolev spaces on metrizable groups | Zendy

Przemysław Górka | Zendy; Tomasz Kostrzewa | Zendy

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A second look of Sobolev spaces on metrizable groups

Author(s) -

Przemysław Górka,

Tomasz Kostrzewa

Publication year - 2020

Publication title -

annales academiae scientiarum fennicae mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.865

H-Index - 37

eISSN - 1798-2383

pISSN - 1239-629X

DOI - 10.5186/aasfm.2020.4507

Subject(s) - sobolev space , metrization theorem , mathematics , pure mathematics , interpolation space , mathematical analysis , functional analysis , chemistry , biochemistry , gene , separable space

We continue our study of Sobolev spaces on locally compact abelian groups. In this paper we mainly focus on the case of metrizable groups. We show the density of the Bruhat–Schwartz space in Sobolev space. We prove the trace theorem on the cartesian product of topological groups. The comparison of Sobolev and fractional Sobolev spaces are given. In particular, it is proved that in the case of any abelian connected Lie group Sobolev and fractional Sobolev spaces coincide. Most of the theorems are illustrated by p-adic groups.

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