A bootstrapping approach to jump inequalities and their applications
Classical Analysis and ODEs
2020-03-25 v2
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 -variational estimates, previously known for , to end-point results for the jump quasi-seminorm corresponding to . This is applied to the dimension-free results recently obtained by the first two authors in collaboration with Bourgain and Wr\'obel (arXiv:1708.04639 and arXiv:1804.07679), and also to operators of Radon type treated by Jones, Seeger, and Wright.
Keywords
Cite
@article{arxiv.1808.09048,
title = {A bootstrapping approach to jump inequalities and their applications},
author = {Mariusz Mirek and Elias M. Stein and Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:1808.09048},
year = {2020}
}
Comments
25 pages, small corrections