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

TL;DR

This paper generalizes classical results on bandlimited multipliers to vector-valued and matrix-weighted $L^p$ spaces, establishing boundedness under matrix Muckenhoupt $A_p$ conditions for $0<p extless=1.

Contribution

It extends Triebel's boundedness results for bandlimited multipliers to matrix-weighted $L^p$ spaces with $0<p extless=1$, incorporating matrix Muckenhoupt $A_p$ conditions.

Findings

Boundedness of bandlimited multipliers on matrix-weighted $L^p$ spaces for $0<p extless=1$.

Extension of classical scalar results to vector-valued and matrix-weighted settings.

Verification of boundedness under matrix Muckenhoupt $A_p$-condition.

Abstract

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