Littlewood-Paley theory for matrix-weighted function spaces (Q2035582)

In this paper the authors define the vector-valued matrix-weighted Triebel-Lizorkin spaces, which include the matrix-weighted \(L^p\) and Sobolev spaces, with the matrix weight belonging to the \(A_{p}\) class. The authors give characterizations of these space via the wavelet transform and \(\varphi\)-transform coefficients. The authors also characterize these spaces in terms of reducing operators associated with the weight.