(𝑃,𝑄) complex hypercontractivity

Proceedings of the American Mathematical Society 2026

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Authors: Paata Ivanisvili, Pavlos Kalantzopoulos
DOI: 10.1090/proc/17596
Cited by: 0
References: 12

Abstract

Let ΞΎ \xi be a standard normal random vector in R k \mathbb {R}^{k} . Under some mild growth and smoothness assumptions on any increasing P , Q : [ 0 , ∞ ) β†’ [ 0 , ∞ ) P, Q : [0, \infty ) \to [0, \infty ) we show ( P , Q ) (P,Q) complex hypercontractivity Q βˆ’ 1 ( E Q ( | T z f ( ΞΎ ) | ) ) ≀ P βˆ’ 1 ( E P ( | f ( ΞΎ ) | ) ) \begin{equation*} Q^{-1}(\mathbb {E} Q(|T_{z}f(\xi )|))\leq P^{-1}(\mathbb {E}P(|f(\xi )|)) \end{equation*} holds for all polynomials f : R k β†’ C

Fields of Study & Subjects

Advanced Harmonic Analysis Research Mathematical Inequalities and Applications Mathematical Analysis and Transform Methods

Publication details

Journal / source
Proceedings of the American Mathematical Society
Volume
154
Issue
4
Pages
1557–1575
Publication date
14 January 2026
Language
EN