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 situa...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.展开更多
基金Research supported in part by NSF(Grants DMS-0901569 and DMS-1363324)
文摘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.
