Constructions of regular algebras $L_p^w(G)$

Details Constructions of regular algebras $L_p^w(G)$ Constructions of regular algebras $L_p^w(G)$

2008-02-29

arxiv.org/abs/0802.4333v1

Mat. Sbornik 200, no. 2 (2009), pp. 75-88

Mathematics

Functional Analysis

Submitted to Mat. Sbornik

Scientific paper

Criterion of (Shilov) regularity for weighted algebras $L_1^w(G)$ on a locally compact abelian group $G$ is known by works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation invariant weighted algebras $L_p^w(G)$ with $p>1$. Regular algebras $L_p^w(G)$ are constructed on any sigma-compact abelian group $G$. It was proved earlier by the author that sigma-compactness is necessary (in the abelian case) for the existence of weighted algebras $L_p^w(G)$ with $p>1$.

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