A note on iterated spherical average on Lebesgue spaces. (March 2019)

• Record Type: Journal Article
• Authors: Fan, Dashan; Lou, Zengjian; Wang, Zijian
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 170
• Page End: 183
• Publication Date: 2019-03
• Subjects: 41A17 -- 41A63 -- 42B30; K-functional -- Spherical average -- Wave operator -- Bessel functions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.10.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For the spherical average A and the Laplace operator Δ, we study the iterated operator Δ A N and find the minimal positive integer N to ensure the L 1 R n boundedness of Δ A N . Using a constructive proof, we completely solve a question posted by Belinsky et al. (2003).