A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator. (31st May 2020) - Zhang, Lei; Shi, Shaoguang
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.