Duality of matrix-weighted Besov spaces

Svetlana Roudenko

Studia Mathematica, Tome 162 (2004), p. 129-156 / Harvested from The Polish Digital Mathematics Library

Résumé

We determine the duals of the homogeneous matrix-weighted Besov spaces $Ḃ^{αq}_{p}(W)$ and $ḃ^{αq}_{p}(W)$ which were previously defined in [5]. If W is a matrix $A_{p}$ weight, then the dual of $Ḃ^{αq}_{p}(W)$ can be identified with $Ḃ^{-αq^{\prime }}_{p^{\prime }}(W^{-p^{\prime }/p})$ and, similarly, $[ḃ^{αq}_{p}(W)]* ≈ ḃ^{-αq^{\prime }}_{p^{\prime }}(W^{-p^{\prime }/p})$. Moreover, for certain W which may not be in the $A_{p}$ class, the duals of $Ḃ^{αq}_{p}(W)$ and $ḃ^{αq}_{p}(W)$ are determined and expressed in terms of the Besov spaces $Ḃ^{-αq^{\prime }}_{p^{\prime }}({A^{-1}_{Q}})$ and $ḃ^{-αq^{\prime }}_{p^{\prime }}({A_{Q}^{-1}})$, 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.

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Publié le : 2004-01-01

Zbl 1067.42015

EUDML-ID : urn:eudml:doc:284515