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

• Mariusz Mirek ^[1] ; Tomasz Z. Szarek ^[2] ; James Wright ^[3]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  2. [2] BCAM-Basque Center for Applied Mathematics
  3. [3] Maxwell Institute of Mathematical Sciences and The School of Mathematics, The University of Edinburgh

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº Extra 7, 2022 (Ejemplar dedicado a: Special issue in honor of Antonio Córdoba and José Luis Fernández), págs. 2249-2284
• Idioma: inglés
• DOI: 10.4171/RMI/1383
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• Resumen

  • 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