A sharp analog of Young’s inequality on SN and related entropy inequalities

By Eric A. Carlen, Elliott H. Lieb, Michael Loss. 2004

172 citations recorded by the source corpus.

We prove a sharp analog of Young’s inequality on SN, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This strategy also works for the generalization of Young’s inequality on RN to more than three functions, and leads to significant new information about the optimizers and the constants.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/57c9f23c208be76796c4c4386b08f8dd9c8cf5ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities (2005, unknown): “Carlen, Lieb and Loss [7] gave an alternative”
On Kac's chaos and related problems (2012, background): “27) was first proved in [18] with k = 1.”
On the multilinear restriction and Kakeya conjectures (2005, background): “) We also remark that closely related monotonicity arguments for gaussians are effective in analysing the Brascamp-Lieb inequalities [11], [4]; see Remark 3.”
Heat-flow monotonicity of Strichartz norms (2008, methodology): “An alternative method of proof, used in [Carlen et al. 2004] and [Bennett et al. 2008a], is based on the divergence theorem and produces the explicit formula 3′(t)= 14 ∫ Rn ∣∣∇(log et1 f1)−∇(log et1 f2)∣∣2(et1 f1)1/2(et1 f2)1/2 (2-1) for each t > 0, provided f1 and f2 are sufficiently well behaved…”
Monotonicity and its analytic and geometric implications (2012, unknown): “[7]”