Duality of matrix-weighted Besov spaces

Volume 160 / 2004

Svetlana Roudenko Studia Mathematica 160 (2004), 129-156 MSC: Primary 42B25, 42B35, 46A20, 46B10; Secondary 47B37, 47B38. DOI: 10.4064/sm160-2-3


We determine the duals of the homogeneous matrix-weighted Besov spaces $\displaystyle \dot{B}^{\alpha q}_p(W)$ and $\displaystyle \dot{b}^{\alpha q}_p(W)$ which were previously defined in [5]. If $W$ is a matrix $A_p$ weight, then the dual of $\dot{B}^{\alpha q}_p(W)$ can be identified with $\displaystyle \dot{B}^{-\alpha q'}_{p'}(W^{-p'/p})$ and, similarly, $\displaystyle [\dot{b}^{\alpha q}_p(W)]^* \approx \dot{b}^{-\alpha q'}_{p'}(W^{-p'/p})$. Moreover, for certain $W$ which may not be in the $A_p$ class, the duals of $\dot{B}^{\alpha q}_p(W)$ and $\dot{b}^{\alpha q}_p(W)$ are determined and expressed in terms of the Besov spaces $\displaystyle \dot{B}^{-\alpha q'}_{p'}(\{A^{-1}_Q\})$ and $\displaystyle \dot{b}^{-\alpha q'}_{p'}(\{A_Q^{-1}\})$, which we define in terms of reducing operators $\{A_Q\}_Q$ associated with $W$. We also develop the basic theory of these reducing operator Besov spaces. Similar results are shown for inhomogeneous spaces.


  • Svetlana RoudenkoMathematics Department
    Duke University
    Durham, NC 27708, U.S.A.

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image