Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem

In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p ∈ (1, ∞) is established.