Duality of matrix-weighted Besov spaces

Svetlana Roudenko. "Duality of matrix-weighted Besov spaces." Studia Mathematica 160.2 (2004): 129-156. <http://eudml.org/doc/284515>.

@article{SvetlanaRoudenko2004,
abstract = {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.},
author = {Svetlana Roudenko},
journal = {Studia Mathematica},
keywords = {Besov spaces; matrix weights; duality; reducing operators; -condition; doubling measure; -transform},
language = {eng},
number = {2},
pages = {129-156},
title = {Duality of matrix-weighted Besov spaces},
url = {http://eudml.org/doc/284515},
volume = {160},
year = {2004},
}

TY - JOUR
AU - Svetlana Roudenko
TI - Duality of matrix-weighted Besov spaces
JO - Studia Mathematica
PY - 2004
VL - 160
IS - 2
SP - 129
EP - 156
AB - 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.
LA - eng
KW - Besov spaces; matrix weights; duality; reducing operators; -condition; doubling measure; -transform
UR - http://eudml.org/doc/284515
ER -