2014/09/20 by Paolo Da Pelo, Da Pelo, Paolo, Alberto Lanconelli +3
Mathematics · #60H07 #60H30 #Advanced Harmonic Analysis Research #Analytic Number Theory Research #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1409.5861
openalex publication_date 2014/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the Beckner's type Poincar 'e inequality citeBeckner to a\nlarge class of probability measures on an abstract Wiener space of the form\n\μ\⋆\ν, where \μ is the reference Gaussian measure and \ν is a\nprobability measure satisfying a certain integrability condition. As the\nBeckner inequality interpolates between the Poincar 'e and logarithmic Sobolev\ninequalities, we utilize a family of products for functions which interpolates\nbetween the usual point-wise multiplication and the Wick product. Our approach\nis based on the positivity of a quadratic form involving Wick powers and\nintegration with respect to those convolution measures. Our\ndimension-independent results are compared with some very recent findings in\nthe literature. In addition, we prove that in the finite dimensional case the\nclass of densities of convolutions measures satisfies a point-wise covariance\ninequality.\n