In d=3, the maximal estimate (1.8) is proved for all s > max{s_d(q), s_d(2β)}, confirming the conjecture; sharp β-ranges are also obtained for d≥4 and d=2.
Orthonormal Strichartz estimates for Schr\"odinger operator and their applications to infinitely many particle systems
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abstract
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory by Kato. We also deduce the refined Strichartz estimates for the Schr\"odinger operator in terms of the Besov space. Finally we prove the global existence of a solution for the Hartree equation with electromagnetic potentials describing the dynamics of infinitely many fermions. This would be the first result on the orthonormal Strichartz estimates for the Schr\"odinger operator with general time-independent potentials including very short range and inverse square type potentials.
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Maximal estimates for orthonormal systems of wave equations with sharp regularity
In d=3, the maximal estimate (1.8) is proved for all s > max{s_d(q), s_d(2β)}, confirming the conjecture; sharp β-ranges are also obtained for d≥4 and d=2.