  Two regularity criteria are established to highlight which Littlewood-Paley
frequencies play an essential role in possible singularity formation in a
Leray-Hopf weak solution to the Navier-Stokes equations in three spatial
dimensions. One of these is a frequency localized refinement of known
Ladyzhenskaya-Prodi-Serrin-type regularity criteria restricted to a finite
window of frequencies the lower bound of which diverges to $+\infty$ as $t$
approaches an initial singular time.
