English

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 rr-variational estimates, previously known for r>2r>2, to end-point results for the jump quasi-seminorm corresponding to r=2r=2. 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