$γ$-Valued Stein--Tomas Restriction for Schatten Classes

Let $Σ\subset\mathbb R^3$ be a compact $C^2$ hypersurface with nonvanishing Gaussian curvature. We prove the sharp matrix-dimension-independent Schatten-valued Stein--Tomas range \[ R_Σ:L^p(\mathbb R^3;S^a)\longrightarrowγ(L^2(Σ),S^a), \qquad 1<a<\infty,\quad 1\le p\le\min\{a,4/3\}. \] The core endp