A Sharp analog of Young's Inequality on Sⁿ and Related Entropy Inequalities

الأصل · EN

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.