m at h . FA ] 2 A ug 2 00 4 A Sharp analog of Young ’ s Inequality on S N and Related Entropy Inequalities
نویسندگان
چکیده
Abstract We prove a sharp analog of Young’s inequality on S , 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 R to more than three functions, and leads to significant new information about the optimizers and the constants.
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