Estimates for the square variation of partial sums of Fourier series and their rearrangements

DOI10.1016/j.jfa.2011.12.007zbMath1239.42027arXiv1106.0871OpenAlexW2964279967MaRDI QIDQ765902

D. Kharzeev

Publication date: 22 March 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0871

zbMATH Keywords

Fourier seriesorthonormal systemp-variation

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Probabilistic methods for one variable harmonic analysis (42A61)

Related Items (11)

Discrete analogues of maximally modulated singular integrals of Stein-Wainger type ⋮ Refinements of Gál's theorem and applications ⋮ Pointwise ergodic theorems for non-conventional bilinear polynomial averages ⋮ An exact asymptotic for the square variation of partial sum processes ⋮ A variational Barban-Davenport-Halberstam theorem ⋮ The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example -- an improvement of Menshov-Rademacher theorem ⋮ Variational bounds for a dyadic model of the bilinear Hilbert transform ⋮ A bootstrapping approach to jump inequalities and their applications ⋮ Jump inequalities for translation-invariant operators of Radon type on \(\mathbb{Z}^d\) ⋮ \(\ell^p(\mathbb{Z}^d)\)-estimates for discrete operators of Radon type: maximal functions and vector-valued estimates ⋮ On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective

Cites Work

• A variation norm Carleson theorem
• An exact asymptotic for the square variation of partial sum processes
• The \(p\)-variation of partial sum processes and the empirical process
• Existence of almost everywhere convergent rearrangements for Fourier series of \(L_ 2\) functions
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Variation inequalities for the Fejér and Poisson kernels
• Probability Inequalities for Sums of Bounded Random Variables
• On an Inequality of Hoeffding
• Maximal functions associated to filtrations
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