JournalsrmiVol. 38, No. 7pp. 2249–2284

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

  • Mariusz Mirek

    Uniwersytet Wrocławski, Poland; Rutgers University, Piscataway; Institute for Advanced Study, Princeton, USA

  • Tomasz Z. Szarek

    BCAM-Basque Center for Applied Mathematics, Bilbao, Spain; Uniwersytet Wrocławski, Poland

  • James Wright

    University of Edinburgh, UK
Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives cover
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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.

Cite this article

Mariusz Mirek, Tomasz Z. Szarek, James Wright, Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives. Rev. Mat. Iberoam. 38 (2022), no. 7, pp. 2249–2284

DOI 10.4171/RMI/1383