Arazy's conjecture concerning Schur multipliers: revisited and resolved

Let $\mathcal{S}^ r$ denote the Schatten--von Neumann class and let $S_{Ψ_{f,λ}}$ be the Schur--Hadamard multiplier whose symbol is the divided-difference matrix of $f$ along $λ$. Let $0<α,r<\infty$, let $f\in C^1([-1,1])$ satisfy $f(0)=0$, $|f'(t)|\lesssim |t|^α$, and let $λ\in\ell^r$ be real with