Analysis & PDE
- Anal. PDE
- Volume 10, Number 5 (2017), 1255-1284.
A sparse domination principle for rough singular integrals
We prove that bilinear forms associated to the rough homogeneous singular integrals
where has vanishing average and , and to Bochner–Riesz means at the critical index in are dominated by sparse forms involving averages. This domination is stronger than the weak- estimates for and for Bochner–Riesz means, respectively due to Seeger and Christ. Furthermore, our domination theorems entail as a corollary new sharp quantitative -weighted estimates for Bochner–Riesz means and for homogeneous singular integrals with unbounded angular part, extending previous results of Hytönen, Roncal and Tapiola for . Our results follow from a new abstract sparse domination principle which does not rely on weak endpoint estimates for maximal truncations.
Anal. PDE, Volume 10, Number 5 (2017), 1255-1284.
Received: 19 January 2017
Accepted: 24 April 2017
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Conde-Alonso, José M.; Culiuc, Amalia; Di Plinio, Francesco; Ou, Yumeng. A sparse domination principle for rough singular integrals. Anal. PDE 10 (2017), no. 5, 1255--1284. doi:10.2140/apde.2017.10.1255. https://projecteuclid.org/euclid.apde/1510843500