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
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10.1512/iumj.2004.53.2483
10.1512/iumj.2004.53.2483
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Indiana Univ. Math. J. 53 (2004) 1225 - 1254
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