Abstract
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.
Citation
José M. Conde-Alonso. Amalia Culiuc. Francesco Di Plinio. Yumeng Ou. "A sparse domination principle for rough singular integrals." Anal. PDE 10 (5) 1255 - 1284, 2017. https://doi.org/10.2140/apde.2017.10.1255
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