Aspects of the Kahane–Salem–Zygmund inequalities in Banach spaces

Author:

Defant Andreas,Mastyło MieczysławORCID

Abstract

AbstractThe main aim of this work is to discuss several different approaches to the celebrated Kahane–Salem–Zygmund inequalities. In particular, we prove estimates for exponential Orlicz norms of averages $$\sup _{1\le j\le N}\Big |\sum _{i=1}^K a_i(j) \gamma _i\Big |\,,$$ sup 1 j N | i = 1 K a i ( j ) γ i | , where $$ (a_i(j)) \in \ell _\infty ^N, \, 1 \le i \le K$$ ( a i ( j ) ) N , 1 i K and the $$(\gamma _i)$$ ( γ i ) form a sequence of real or complex subgaussian random variables. Lifting these inequalities to finite dimensional Banach spaces, we get some new Kahane–Salem–Zygmund type inequalities—in particular, for spaces of subgaussian random polynomials and multilinear forms on finite dimensional Banach spaces, and also for subgaussian random Dirichlet polynomials.

Funder

Narodowe Centrum Nauki

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An Explicit Croot-Łaba-Sisask Lemma Free of Probabilistic Language;Bulletin of the Brazilian Mathematical Society, New Series;2024-04-25

2. Coefficients of Multilinear Forms on Sequence Spaces;Bulletin of the Brazilian Mathematical Society, New Series;2023-08-05

3. VARIANTS OF A MULTIPLIER THEOREM OF KISLYAKOV;Journal of the Institute of Mathematics of Jussieu;2022-09-01

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