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A bootstrapping
approach to jump inequalities and their applications
Mariusz Mirek, Elias M. Stein and Pavel Zorin-Kranich |
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Vol. 13 (2020), No. 2, 527–558
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Abstract |
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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 -variational estimates, previously known for , to endpoint results for the jump quasiseminorm corresponding to . 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
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Mathematical Subject Classification 2010
Primary: 42B25
Secondary: 42B20, 46B06
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Milestones
Received: 29 August 2018
Revised: 23 December 2018
Accepted: 23 February 2019
Published: 19 March 2020
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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 |
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| Pavel Zorin-Kranich | |
| Mathematisches Institut Universität Bonn Bonn Germany |
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