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We establish new Strichartz estimates for orthonormal families of initialdata in the case of the wave, Klein-Gordon and fractional Schr\"odingerequations. Our estimates extend those of Frank-Sabin in the case of the waveand Klein-Gordon equations, and generalize work of Frank-Lewin-Lieb-Seiringerand Frank-Sabin for the Schr\"{o}dinger equation. Due to a certain technicalbarrier, except for the classical Schr\"odinger equation, the Strichartzestimates for orthonormal families of initial data have not previously beenestablished up to the sharp summability exponents in the full range ofadmissible pairs. We obtain the optimal estimates in various notable cases andimprove the previous results. The main novelty of this paper is the use ofestimates for weighted oscillatory integrals which we combine with an approachdue to Frank and Sabin. This strategy also leads us to proving new estimatesfor weighted oscillatory integrals with optimal decay exponents which webelieve to be of wider independent interest. Applications to the theory ofinfinite systems of Hartree type, weighted velocity averaging lemmas forkinetic transport equations, and refined Strichartz estimates for data in Besovspaces are also provided.

Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates