Near-extremizers of Young's Inequality for R^d

Abstract

If a pair of functions nearly extremizes Young's convolution inequality for R^d, with all three exponents finite and strictly greater than 1, then each function is close in norm to a Gaussian. The proof relies on the Riesz-Sobolev rearrangement inequality and in particular, on an approximate inverse Riesz-Sobolev inequality established in a companion paper.

References in corpus (4)

• On extremals for a Radon-like transform
• An Approximate Inverse Riesz-Sobolev Inequality
• Near-extremizers of Young's inequality for discrete groups
• Large values of the Gowers-Host-Kra seminorms

Cited by in corpus (12)

• Forward and Reverse Entropy Power Inequalities in Convex Geometry
• Gaussian optimizers for entropic inequalities in quantum information
• A sharpened Hausdorff-Young inequality
• Near Equality in the Brunn-Minkowski Inequality
• Near equality in the two-dimensional Brunn-Minkowski inequality
• A sharpened Riesz-Sobolev inequality
• On Restricting Cauchy-Pexider Equations to Submanifolds
• On an extremization problem concerning Fourier coefficients
• Near equality in the Riesz-Sobolev inequality in higher dimensions
• Stability of trace theorems on the sphere
• On nearly radial product functions
• A constrained optimization problem for the Fourier transform: Existence