Almost-orthogonal Strichartz estimates and radial improvements

Abstract: We extend the Schatten-duality principle from orthonormal systems to (almost-orthogonal) Bessel families and apply it to prove sharp and improved Bessel-family Strichartz estimates for the Kadomtsev--Petviashvili, Zakharov--Kuznetsov, and radial Schrödinger equations. In particular, for the Schrödinger equation, we establish an improved estimate in a larger radial range of space-time exponents, not from dispersive estimates as in the KP/ZK models, but from direct robust Schatten estimates, using some vector-valued multi-product trace formula and multilinear weighted fractional integral formula. To the best of our knowledge, this is the first radial improvement for systems, and the almost-orthogonal estimates are also new to the literature. We also derive necessary conditions.