Matrix-weighted Besov spaces and conditions of $A_p$ type for $0 < p leq 1$ Michael FrazierSvetlana Roudenko 42B3547B3842B2546A20matrix weights$A_p$ classBesov spacesCalderon-Zygmund operatorsHilbert transformdoubling measurereducing operatorsvarphi-transform 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. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2483 10.1512/iumj.2004.53.2483 en Indiana Univ. Math. J. 53 (2004) 1225 - 1254 state-of-the-art mathematics http://iumj.org/access/