Regularity Properties and Lipschitz Spaces Adapted to High-Order Schrödinger Operators

Let be the high-order Schrödinger operator (−Δ)2+V2, where V is a non-negative potential satisfying reverse Hölder inequality (RHq), with q>n/2 and n≥5. In this paper, we prove that when 0<α≤2−n/q, adapted Lipschitz spaces Λα/4L considered are equivalent to space CLα associated L=−Δ+V. order obtain characterization, should make use of some results (−Δ)2. We also regularity properties fractional powers (positive negative) ℒ, Riesz transforms, Bessel potentials multipliers Laplace transforms type operators.