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Keywords:
Triebel-Lizorkin space; duality; weighted multi-parameter
Triebel-Lizorkin space; duality; weighted multi-parameter
Summary:
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 $0<p\leq 1$ has been proved in Ding, Zhu (2017). In this paper, for $1<p<\infty $, $0<q<\infty $ we establish its dual space $\dot H^{\alpha ,q}_{p}(\omega ;\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$.
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