The Littlewood-Paley type g-function, the Lusin type s-function, and their applications

Speaker：Shaolin Chen (Hengyang Normal University)

Time：2026-5-27 16:00

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

The purpose of this talk is twofold. First, we investigate several properties of the Littlewood-Paley type g-function and the Lusin type s-function associated with the invariant Laplacian (or Laplace-Beltrami) operator. Our work extends and refines some of the main results established by Kwon [Trans. Am. Math. Soc. 355: 1269-1294, 2003]. Second, we employ these g- and  s-functions to study the Riesz conjugate functions theorem. As a consequence, we generalize and improve the main results of Liu and Zhu [Adv. Math. 434: 109321, 2023]. Additionally, our results provide a partial answer to an open problem posed by Astala and Koskela [Pure Appl. Math. Q. 7: 19-50, 2011].