Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives

Mariusz  Mirek; Tomasz Z. Szarek; James Wright

doi:10.4171/RMI/1383

Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives

Mariusz Mirek, Tomasz Z. Szarek , James Wright

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.

Original language	English
Pages (from-to)	2249-2284
Number of pages	36
Journal	Revista Matemática Iberoamericana
Volume	38
Issue number	7
DOIs	https://doi.org/10.4171/RMI/1383
Publication status	Published - 23 Dec 2022

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10.4171/RMI/1383

https://arxiv.org/abs/2209.01309

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title = "Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives",

abstract = "In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.",

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AB - In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.

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DO - 10.4171/RMI/1383

M3 - Article

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Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives

Abstract

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