Event № 112
In this talk we propose algebraic criteria that yield sharp Hölder and reverse Hölder types of inequalities for the product of functions on Gaussian random vectors with arbitrary covariance structure. While the lower inequality appears to be new, we prove that the upper inequality gives an equivalent formulation for the Brascamp-Lieb inequality. We will see that this result generalizes, Hölder's inequality, Nelson's hypercontractivity and the sharp Young inequality as well as their reverse forms. Moreover, we will give one more application: Barthe's and Prekopa-Leindler inequalities.
Based on a joint work with Wei-Kuo Chen and Grigoris Paouris