A HÖLDER–YOUNG–LIEB INEQUALITY FOR NORMS OF GAUSSIAN WICK PRODUCTS

DOI10.1142/S0219025711004456zbMath1230.44002arXiv1101.2947MaRDI QIDQ3095478

Aurel I. Stan, Alberto Lanconelli, Paolo Da Pelo

Publication date: 2 November 2011

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.2947

zbMATH Keywords

Wick productexponential functionsconvolution productHölder inequalityYoung inequalitysecond quantization operatorLieb inequality

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) White noise theory (60H40) Inequalities for sums, series and integrals (26D15)

Related Items (10)

Prohorov-type local limit theorems on abstract Wiener spaces ⋮ Standardizing densities on Gaussian spaces ⋮ A new approach to Poincaré-type inequalities on the Wiener space ⋮ A note on Gamma Wick products ⋮ WICK CALCULUS FOR THE SQUARE OF A GAUSSIAN RANDOM VARIABLE WITH APPLICATION TO YOUNG AND HYPERCONTRACTIVE INEQUALITIES ⋮ Contractivity of gamma Wick products ⋮ A note on a local limit theorem for Wiener space valued random variables ⋮ A sharp interpolation between the Hölder and Gaussian Young inequalities ⋮ Rate of convergence for Wong-Zakai-type approximations of Itô stochastic differential equations ⋮ A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS

Cites Work

• Gaussian kernels have only Gaussian maximizers
• Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Inequalities in Fourier analysis
• White noise calculus and Fock space
• A sharp analog of Young's inequality on \(S^N\) and related entropy inequalities
• BEST CONSTANTS IN NORMS OF RETARDED WICK PRODUCTS
• Some Norm Inequalities for Gaussian Wick Products
• BEST CONSTANTS IN NORMS OF WICK PRODUCTS

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