The aim of this paper is to prove the duality of Triebel–Lizorkin spaces \( F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }\). First, we prove the duality of associated sequence spaces. The result follows from the so-called \(\varphi \)-transform characterization in the sense of Frazier and Jawerth.

中文翻译：

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关于可变Triebel–Lizorkin空间的对偶性

本文的目的是证明Triebel–Lizorkin空间\（F_ {1，q \ left（\ cdot \ right）} ^ {\ alpha \ left（\ cdot \ right）} \）的对偶性。首先，我们证明了相关序列空间的对偶性。结果来自于Frazier和Jawerth的所谓\（\ varphi \）-变换表征。