Trace Class Norm Inequalities
Man Wah Wong · Birkhäuser Basel eBooks · 2002
As a sequel to Chapter 13, we prove in this chapter that the constant $$\tfrac{4}{{{{c}_{\varphi }}}}$$ in Proposition 13.1 can be improved to $$\tfrac{1}{{{{c}_{\varphi }}}}$$ and obtain a lower bound for the norm ‖L F,φ ‖ S 1 of the localization operator L F,φ : X → X in S 1 in terms of the function F φ on G defined by 14.1 $$\begin{array}{*{20}{c}} {{{F}_{\varphi }}(g) = ({{L}_{{F,\varphi }}}\pi (g)\varphi ,\pi (g)\varphi ),} & {g \in G.} \\ \end{array}$$ g ∈ G.