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.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics
- Dimension-free estimate
- Jump inequality