Bandlimited Multipliers on Matrix-Weighted \(L^p\)-Spaces

We extend a classical result by Triebel on boundedness of bandlimited multipliers on \(L^p({\mathbb R}^n)\) $L^p({\mathbb{R}}^n)$ , \(0<p\le 1\) $0<p\le 1$ , to a vector-valued and matrix-weighted setting with boundedness of the bandlimited multipliers obtained on \(L^p(W)\) $L^p(W)$ , \(0<p\le 1\) $0<p\le 1$ , for matrix-weights \(W:{\mathbb R}^n\rightarrow \mathbb {C}^{N\times N}\) $W:{\mathbb{R}}^n\to {\mathbb{C}}^{N\times N}$ that satisfy a matrix Muckenhoupt \(A_p\) $A_p$ -condition.