Equivalences of (quasi-)norms in a certain vector-valued function space and its applications to multilinear operators

In this talk we will study some (quasi-)norm equivalences, involving L^p(ℓ^q) norm, in a certain vector-valued function space and extend the equivalences to p = ∞ and 0 < q < ∞ in the scale of Triebel-Lizorkin spaces. As an immediate consequence of our results, ‖f‖_BMO can be written as L^∞(ℓ²) norm of a variant of f. We will also discuss some applications to multilinear operators.