Endpoint variation and jump inequalities for rough singular integrals
Abstract
In this article, we prove weak type $(1,1)$ bounds for the variation and jump operators corresponding to the family of truncations of singular integrals with rough kernels. This resolves an open question raised by Jones, Seeger and Wright (Trans. Amer. Math. Soc. (2008)). Moreover, as an immediate consequence of the variational estimate, we recover the weak type $(1,1)$ boundedness of the maximal truncation operator corresponding to singular integrals with rough kernels.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 February 2026
- Language
- EN
- Document type
- Preprint