Abstract
Let L = − Δ + V be a Schrödinger operator on ℝ n , where Δ denotes the Laplace operator ∑ i = 1 n ∂ 2 / ∂ x i 2 and V is a nonnegative potential belonging to a certain reverse Hölder class R H q ℝ n with q > n / 2 . In this paper, by the regularity estimate of the fractional heat kernel related with L , we establish the quantitative weighted boundedness of Littlewood-Paley functions generated by fractional heat semigroups related with the Schrödinger operators.
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