Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields

In this paper, we combine the argument of [12] and [27] to prove the maximal estimates for fractional Schrödinger equations $(i\partial_t+\mathcal{L}_{\mathbf{A}}^{\fracα2})u=0$ in the purely magnetic fields which includes the Aharonov-Bohm fields. The proof is based on the cluster spectral measure estimates. In particular $α=1$, the maximal estimate for wave equation is sharp up to the endpoint.

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