A bootstrapping approach to jump inequalities and their applications

Mariusz Mirek; Elias M. Stein; Pavel Zorin-Kranich

doi:10.2140/apde.2020.13.527

A bootstrapping approach to jump inequalities and their applications

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

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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 Wrobel, and also to operators of Radon type treated by Jones, Seeger, and Wright.

Original language	English (US)
Pages (from-to)	527-558
Number of pages	32
Journal	Analysis and PDE
Volume	13
Issue number	2
DOIs	https://doi.org/10.2140/apde.2020.13.527
State	Published - 2020

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

Keywords

Dimension-free estimate
Jump inequality

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10.2140/apde.2020.13.527

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A bootstrapping approach to jump inequalities and their applications

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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