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Note on duality of weighted multi-parameter Triebel-Lizorkin spaces
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 763-779 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces $\dot F^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$. This space has been introduced and the result $$(\dot F^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}}))^{\ast }= {\rm CMO}^{-\alpha ,q'}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$$ for $0$ has been proved in Ding, Zhu (2017). In this paper, for $1$, $0$ we establish its dual space $\dot H^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$.
We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces $\dot F^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$. This space has been introduced and the result $$(\dot F^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}}))^{\ast }= {\rm CMO}^{-\alpha ,q'}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$$ for $0$ has been proved in Ding, Zhu (2017). In this paper, for $1$, $0$ we establish its dual space $\dot H^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$.
DOI : 10.21136/CMJ.2019.0509-17
Classification : 42B25, 42B35
Keywords: Triebel-Lizorkin space; duality; weighted multi-parameter 
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     title = {Note on duality of weighted multi-parameter {Triebel-Lizorkin} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {763--779},
     year = {2019},
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Ding, Wei; Chen, Jiao; Niu, Yaoming. Note on duality of weighted multi-parameter Triebel-Lizorkin spaces. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 763-779. doi: 10.21136/CMJ.2019.0509-17

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