A bootstrapping approach to jump inequalities and their applications
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 end-point results for the jump quasi-seminorm 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 (arXiv:1708.04639 and arXiv:1804.07679), and also to operators of Radon type treated by Jones, Seeger, and Wright.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.09048
- arXiv:
- arXiv:1808.09048
- Bibcode:
- 2018arXiv180809048M
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 42B25 (Primary) 42B20;
- 46B06 (Secondary)
- E-Print:
- 25 pages, small corrections