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Brascamp-Lieb inequalities on compact homogeneous spaces. (English) Zbl 1480.43002

Author’s abstract: We provide a general strategy to construct multilinear inequalities of Brascamp-Lieb type on compact homogeneous spaces of Lie groups. As an application we obtain sharp integral inequalities on the real unit sphere involving functions with some degree of symmetry.

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
43A85 Harmonic analysis on homogeneous spaces
52A40 Inequalities and extremum problems involving convexity in convex geometry
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