A bootstrapping approach to jump inequalities and their applications
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
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 [math] -variational estimates, previously known for [math] , to endpoint results for the jump quasiseminorm corresponding to [math] . This is applied to the dimension-free results recently obtained by the first two authors in collaboration with Bourgain, and Wróbel, and also to operators of Radon type treated by Jones, Seeger, and Wright.
Topics & Concepts
MathematicsJumpBootstrapping (finance)Type (biology)Applied mathematicsPrincipal (computer security)InequalityHarmonicPrincipal component analysisHarmonic analysisClass (philosophy)Calculus (dental)Work (physics)Step detectionAdvanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsNumerical methods in inverse problems