Duality of matrix-weighted Besov spaces

• Autorzy: Svetlana Roudenko
• Języki publikacji: EN

Abstrakty

EN

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 $Ḃ^{-αq'}_{p'}(W^{-p'/p})$ and, similarly, $[ḃ^{αq}_{p}(W)]* ≈ ḃ^{-αq'}_{p'}(W^{-p'/p})$. 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 $Ḃ^{-αq'}_{p'}({A^{-1}_{Q}})$ and $ḃ^{-αq'}_{p'}({A_{Q}^{-1}})$, 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.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 42B35: Function spaces arising in harmonic analysis
• 47B38: Operators on function spaces (general)
• 46A20: Duality theory
• 46B10: Duality and reflexivity
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 2
• Strony: 129-156

Daty

wydano

2004

Twórcy

autor

Svetlana Roudenko

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

Identyfikatory

DOI

10.4064/sm160-2-3