Orthonormal Strichartz inequalities and their applications on abstract measure spaces

2024/09/21 by Feng, Guoxia, Mondal, Shyam Swarup, Song, Manli +1 · 3 citations
#35B65 #47D08 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42B37

paper · doi:10.48550/arxiv.2409.14044

Abstract

The main objective of this paper is to extend certain fundamental inequalities from a single function to a family of orthonormal systems. In the first part of the paper, we consider a non-negative, self-adjoint operator L on L²(X,μ), where (X,μ) is a measure space. Under the assumption that the kernel K_it(x,y) of the Schrödinger propagator e^itL satisfies a uniform L^∞-decay estimate of the form \beginequation* sup_{x,y∈ X}|K_it(x,y)|\lesssim |t|^-(n)/(2), |t|

Cited by

• Decay estimates for a class of dispersive equations with partial inverse-square potentials
• Restriction Theorem and Strichartz estimate for orthonormal functions associated with the Special Hermite Operator
• Strichartz estimates involving orthonormal systems at the critical summability exponent

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