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Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields

  • Haoran Wang ORCID logo and Jiye Yuan ORCID logo EMAIL logo
Published/Copyright: October 4, 2023

Abstract

In this paper, we combine the arguments of [L. Fanelli, J. Zhang and J. Zheng, Uniform resolvent estimates for Schrödinger operators in critical magnetic fields, Int. Math. Res. Not. IMRN 2023), 10.1093/imrn/rnac362] and [Y. Sire, C. D. Sogge, C. Wang and J. Zhang, Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications, Comm. Partial Differential Equations 47 2022, 6, 1124–1132] to prove the maximal estimates for fractional Schrödinger equations ( i t + 𝐀 α 2 ) 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, for α = 1 , the maximal estimate for wave equation is sharp up to the endpoint.

MSC 2020: 42B25; 35Q40; 35Q41

Communicated by Christopher D. Sogge


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Received: 2023-07-24
Published Online: 2023-10-04
Published in Print: 2024-05-01

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