Qingying Xue

We prove endpoint theorems for one-dimensional bilinear rough singular integrals. Our starting point is a sharp structural characterization of the associated angular multiplier. For every mean-zero $Ω\in L^1(\mathbb{S}^1)$, the finite-part angular multiplier associated with $T_Ω$ has bounded variation if and only if the antipodal even part of $Ω$ belongs to $H^1(\mathbb{S}^1)$.

Wang, Shifen [1] ; Zhang, Chunmei [1] ; Xue, Qingying [2] [1] School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China [2] School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, People’s Republic of China Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs.

This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessReview by Wenjuan Li 1, Huiju Wang 2 and Qingying Xue 3,* 1 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China 2 School of Mathematics and Statistics, Henan University, Kaifeng 475001, China 3 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China * Author to whom correspondence should be addressed.