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Clarkson inequalities on \(L^p(\widehat{G})\) space associated with compact Lie group. (English) Zbl 1455.46030

Summary: We prove Clarkson inequalities for \(L^p(\widehat{G})\) space, which was defined in [M. Ruzhansky and V. Turunen, Int. Math. Res. Not. 2013, No. 11, 2439–2496 (2013; Zbl 1317.22007)]. We also present another proof of reflexivity of this space for \(1<p<\infty \).

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B10 Duality and reflexivity in normed linear and Banach spaces
43A20 \(L^1\)-algebras on groups, semigroups, etc.

Citations:

Zbl 1317.22007
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References:

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