Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 763-779, 2019


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

Wei Ding, Jiao Chen, Yaoming Niu

Received November 4, 2017.   Published online February 18, 2019.

Abstract:  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 $0<p\leq1$ has been proved in Ding, Zhu (2017). In this paper, for $1< p< \infty$, $0< q<\infty$ we establish its dual space $\dot H^{\alpha, q}_p(\omega; \mathbb{R}^{n_1} \times \mathbb{R}^{n_2})$.
Keywords:  Triebel-Lizorkin space; duality; weighted multi-parameter
Classification MSC:  42B25, 42B35
DOI:  10.21136/CMJ.2019.0509-17


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Affiliations:   Wei Ding, School of Sciences, Nantong University, Nantong 226007, P. R. China, e-mail: dingwei@ntu.edu.cn; Jiao Chen (corresponding author), School of Mathematical Sciences, Chongqing Normal University, Chongqing 400000, P. R. China, e-mail: chenjiaobnu@163.com; Yaoming Niu, Faculty of Mathematics, Baotou Teachers' College of Inner Mongolia University of Science and Technology, Baotou 014030, P. R. China, e-mail: nymmath@126.com


 
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