Some remarks on the maximally modulated Calderón-Zygmund operator satisfying $L^r$-Hörmander condition

Abstract

In this work, by recent work of Lerner and Ombrasi (J. Geom. Anal. 30(1): 1011-1027, 2020), we show a maximally modulated singular integral operator which its kernel satisfying $L^r$- Hörmander condition can be dominated by sparse operators. Also, the local exponential decay estimates for these operators are obtained.

arXiv comment11 pages