Czechoslovak Mathematical Journal, first online, pp. 1-13
Hausdorff operator on Morrey spaces and Campanato spaces
Jianmiao Ruan, Dashan Fan, Hongliang Li
Received August 22, 2018. Published online December 27, 2019.
Abstract: We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).
Keywords: Hausdorff operator; Morrey space; Campanato space
Affiliations: Jianmiao Ruan (corresponding author), Department of Mathematics, Zhejiang International Studies University, 299 Liuhe Road, Xihu, Hangzhou 310014, P. R. China, e-mail: rjmath@@163.com; Dashan Fan, Department of Mathematical Sciences, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee WI 53201-0413, USA, e-mail: fan@@uwm.edu; Hongliang Li, Department of Mathematics, Zhejiang International Studies University, 299 Liuhe Road, Xihu, Hangzhou 310014, P. R. China, e-mail: honglli@@126.com