On bandlimited multipliers on matrix-weighted $L^p$-spaces

Abstract

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