Vol. 13, No. 2, 2020

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A bootstrapping approach to jump inequalities and their applications

Mariusz Mirek, Elias M. Stein and Pavel Zorin-Kranich

Vol. 13 (2020), No. 2, 527–558
Abstract

The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of r-variational estimates, previously known for r > 2, to endpoint results for the jump quasiseminorm corresponding to r = 2. This is applied to the dimension-free results recently obtained by the first two authors in collaboration with Bourgain, and Wróbel, and also to operators of Radon type treated by Jones, Seeger, and Wright.

Keywords
dimension-free estimate, jump inequality
Mathematical Subject Classification 2010
Primary: 42B25
Secondary: 42B20, 46B06
Milestones
Received: 29 August 2018
Revised: 23 December 2018
Accepted: 23 February 2019
Published: 19 March 2020
Authors
Mariusz Mirek
Department of Mathematics
Rutgers University
Piscataway, NJ
United States
Instytut Matematyczny
Uniwersytet Wrocławski
Wrocław
Poland
Elias M. Stein
Department of Mathematics
Princeton University
Princeton, NJ
United States
Pavel Zorin-Kranich
Mathematisches Institut
Universität Bonn
Bonn
Germany