Sharp Bounds for Fractional Conjugate Hardy Operator on Higher-Dimensional Product Spaces. (1st May 2020) - Wang, Zequn; Wei, Mingquan; He, Qianjun; Yan, Dunyan
Abstract : In this paper, we obtain the sharp bound for fractional conjugate Hardy operator on higher-dimensional product spaces from L 1 ℝ n 1 × ⋯ × ℝ n m to the space w L Q ℝ n 1 × ⋯ × ℝ n m and L p ℝ n 1 × ⋯ × ℝ n m to the space L q ℝ n 1 × ⋯ × ℝ n m . More generally, the operator norm of the fractional Hardy operator on higher-dimensional product spaces from L P ℝ n 1 × ⋯ × ℝ n m to L Q I ℝ n 1 × ⋯ × ℝ n m is obtained.