Note on duality of weighted multi-parameter Triebel-Lizorkin spaces

Ding, Wei ; Chen, Jiao ; Niu, Yaoming

Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 763-779.

Résumé

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 $\dot H^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$.

Détail

DOI : 10.21136/CMJ.2019.0509-17

Classification : 42B25, 42B35
Keywords: Triebel-Lizorkin space; duality; weighted multi-parameter