Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials - Yu Liu (International Journal of Mathematics and Mathematical Sciences, 2008)
We consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2,  n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1 under the same condition of V.