Near Equality in the Riesz-Sobolev Inequality

Near Equality in the Riesz-Sobolev Inequality

The Riesz-Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of appropriately situated intervals. We characterize ordered triples of subsets of ℝ 1 that nearly realize...

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Veröffentlicht in:Acta mathematica Sinica. English series 2019-06, Vol.35 (6), p.783-814
1. Verfasser: Christ, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Convolution
Equality
Mathematics
Mathematics and Statistics
Upper bounds
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Zusammenfassung:The Riesz-Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of appropriately situated intervals. We characterize ordered triples of subsets of ℝ 1 that nearly realize equality, with quantitative bounds of power law form with the optimal exponent.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-019-8412-7