Regularities of Time-Fractional Derivatives of Semigroups Related to Schrodinger Operators with Application to Hardy-Sobolev Spaces on Heisenberg Groups. (10th October 2020) - Wang, Zhiyong; Sun, Chuanhong; Li, Pengtao
Abstract : In this paper, assume that L = − Δ ℍ n + V is a Schrödinger operator on the Heisenberg group ℍ n, where the nonnegative potential V belongs to the reverse Hölder class B Q / 2 . By the aid of the subordinate formula, we investigate the regularity properties of the time-fractional derivatives of semigroups e − t L t > 0 and e − t L t > 0, respectively. As applications, using fractional square functions, we characterize the Hardy-Sobolev type space H L 1, α ℍ n associated with L . Moreover, the fractional square function characterizations indicate an equivalence relation of two classes of Hardy-Sobolev spaces related with L .