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The dual space of variable weak Hardy space \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\)

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Abstract

In this paper, we introduce a closed subspace \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\) of variable weak Hardy spaces \(H^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\), and give the dual space of \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\) with the variable exponent function \(p(\cdot ): \mathbb {R}^n \rightarrow (0,\infty )\) satisfying the globally log-Hölder continuous condition.

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Notes

  1. In [3], if \(p=1\) and \(L=-\varDelta \) with \(\varDelta \) being the Laplacian operator, then \(H^{1,\infty }_{-\varDelta }({{\mathbb {R}}}^n)=\overline{L_0^1}\) (see [3, Remark 2.14]).

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Authors and Affiliations

  1. Central South University, Changsha, China

    Yao He

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  1. Yao He
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Correspondence to Yao He.

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Communicated by Yong Jiao.

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He, Y. The dual space of variable weak Hardy space \({\mathcal {H}}^{p(\cdot ),\infty }({{\mathbb {R}}}^n)\). Ann. Funct. Anal. 11, 1027–1041 (2020). https://doi.org/10.1007/s43034-020-00068-8

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  • DOI: https://doi.org/10.1007/s43034-020-00068-8

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