A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator. (31st May 2020)

• Record Type: Journal Article
• Authors: Zhang, Lei; Shi, Shaoguang
• Other Names: Liu Lishan Guest Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-05-31
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/3543165
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper is devoted in characterizing the central BMO ℝ n space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol function belongs to the central BMO ℝ n space, then the commutator are bounded on Lebesgue space. Conversely, the boundedness of the commutator implies that the symbol function belongs to the central BMO ℝ n space by exploiting the center symmetry of the Hardy operator deeply.