Analysis & PDE

  • Anal. PDE
  • Volume 10, Number 5 (2017), 1255-1284.

A sparse domination principle for rough singular integrals

José M. Conde-Alonso, Amalia Culiuc, Francesco Di Plinio, and Yumeng Ou

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Abstract

We prove that bilinear forms associated to the rough homogeneous singular integrals

TΩf(x) = p.v.df(x y)Ω( y |y|) |y|d,

where Ω Lq(Sd1) has vanishing average and 1 < q , and to Bochner–Riesz means at the critical index in d are dominated by sparse forms involving (1,p) averages. This domination is stronger than the weak-L1 estimates for TΩ and for Bochner–Riesz means, respectively due to Seeger and Christ. Furthermore, our domination theorems entail as a corollary new sharp quantitative Ap-weighted estimates for Bochner–Riesz means and for homogeneous singular integrals with unbounded angular part, extending previous results of Hytönen, Roncal and Tapiola for TΩ. Our results follow from a new abstract sparse domination principle which does not rely on weak endpoint estimates for maximal truncations.

Article information

Source
Anal. PDE, Volume 10, Number 5 (2017), 1255-1284.

Dates
Received: 19 January 2017
Accepted: 24 April 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843500

Digital Object Identifier
doi:10.2140/apde.2017.10.1255

Mathematical Reviews number (MathSciNet)
MR3668591

Zentralblatt MATH identifier
06740746

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

Keywords
positive sparse operators rough singular integrals weighted norm inequalities

Citation

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


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