Pointwise ergodic theorems for non-conventional bilinear polynomial averages

DOI10.4007/annals.2022.195.3.4zbMath1505.37010arXiv2008.00857OpenAlexW3046458661WikidataQ113692552 ScholiaQ113692552MaRDI QIDQ2171411

Ben Krause, Mariusz Mirek, Terence C. Tao

Publication date: 9 September 2022

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.00857

zbMATH Keywords

circle methodpointwise convergenceinverse theoremsFourier methodsvariational estimatesnon-conventional ergodic averagesadelic integres

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Applications of the Hardy-Littlewood method (11P55) Ergodic theorems, spectral theory, Markov operators (37A30) Convolution, factorization for one variable harmonic analysis (42A85) Trigonometric and exponential sums (general theory) (11L03) Multipliers in one variable harmonic analysis (42A45) Conjugate functions, conjugate series, singular integrals (42A50) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Weyl sums (11L15) Relations between ergodic theory and number theory (37A44) Relations between ergodic theory and harmonic analysis (37A46)

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Trilinear smoothing inequalities and a variant of the triangular Hilbert transform ⋮ On a multi-parameter variant of the Bellow–Furstenberg problem ⋮ Polynomial sequences in discrete nilpotent groups of step 2 ⋮ Polynomial ergodic averages of measure-preserving systems acted by \(\mathbb{Z}^d\) ⋮ Large deviation principle of multiplicative Ising models on Markov-Cayley trees ⋮ Polynomial averages and pointwise ergodic theorems on nilpotent groups ⋮ Joint ergodicity of sequences ⋮ Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives

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