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
A set E ? R^d whose indicator function 1_E has maximal Gowers norm, among all sets of equal measure, is an ellipsoid up to Lebesgue null sets. If 1_E has nearly maximal Gowers norm then E nearly coincides with some el...A set E ? R^d whose indicator function 1_E has maximal Gowers norm, among all sets of equal measure, is an ellipsoid up to Lebesgue null sets. If 1_E has nearly maximal Gowers norm then E nearly coincides with some ellipsoid, in the sense that their symmetric difference has small Lebesgue measure.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.
基金Research supported in part by NSF(Grant DMS-1363324)
文摘A set E ? R^d whose indicator function 1_E has maximal Gowers norm, among all sets of equal measure, is an ellipsoid up to Lebesgue null sets. If 1_E has nearly maximal Gowers norm then E nearly coincides with some ellipsoid, in the sense that their symmetric difference has small Lebesgue measure.
