：Near Equality in the Riesz–Sobolev Inequality论文

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作者（2019）在《Near Equality in the Riesz–Sobolev Inequality》一文中研究指出：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.

Abstract

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.

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