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October 3, 2025Open Access

The Lᵖ-continuity of wave operators for fractional order Schrödinger operators

Key Points

Wave operators are shown to extend to bounded operators on L^p spaces for fractional Schrödinger operators.
The result holds for potentials depending on the dimension n and order α, indicating conditions for boundedness.
Dispersive and Strichartz estimates can be derived as important consequences of the bounded wave operators.
Results apply when n exceeds 2α and α is greater than 1, confirming the significance of the fractional approach.

Abstract

We consider fractional Schrödinger operators H= (-Δ) ^α+V (x) in n dimensions with real-valued potential V when n>2α, α>1. We show that the wave operators extend to bounded operators on Lᵖ (Rⁿ) for all 1 p under conditions on the potential that depend on n and α analogously to the case when α N. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schrödinger operator.

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