IUMJ

Title: Matrix-weighted Besov spaces and conditions of $A_p$ type for $0 < p leq 1$

Authors: Michael Frazier and Svetlana Roudenko

Issue: Volume 53 (2004), Issue 5, 1225-1254

Abstract:

We introduce the matrix weight class $A_p$ for $0 less than p \leq 1$. For $W \in A_p$ we define the continuous and discrete matrix-weighted Besov spaces $\dot{B}^{\alpha q}_{p}(W)$ and $\dot{b}^{\alpha q}_{p}(W)$ and show their equivalence via transforms of wavelet type. We show that appropriate Calderon-Zygmund operators are bounded on $\dot{B}^{\alpha q}_{p}(W)$. Furthermore, we determine the duals of these Besov spaces using the technique of reducing operators.