Wavelet Characterizations of Variable Anisotropic Hardy Spaces

Yao He, Yong Jiao, Jun Liu

Acta Mathematica Sinica ›› 2025, Vol. 41 ›› Issue (1) : 304-326.

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Acta Mathematica Sinica ›› 2025, Vol. 41 ›› Issue (1) : 304-326. DOI: 10.1007/s10114-025-3567-x
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Wavelet Characterizations of Variable Anisotropic Hardy Spaces

  • Yao He1, Yong Jiao1, Jun Liu2
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Abstract

Let p():Rn(0,] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on Rn. Let HAp()(Rn) be the variable anisotropic Hardy space associated with A. In this paper, via first establishing a criterion for affirming some functions being in the space HAp()(Rn), the authors obtain several equivalent characterizations of HAp()(Rn) in terms of the so-called tight frame multiwavelets, which extend the well-known wavelet characterizations of classical Hardy spaces. In particular, these wavelet characterizations are shown without the help of Peetre maximal operators.

Key words

Variable exponent / Hardy space / expansive matrix / wavelet / atom

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Yao He , Yong Jiao , Jun Liu. Wavelet Characterizations of Variable Anisotropic Hardy Spaces. Acta Mathematica Sinica, 2025, 41(1): 304-326 https://doi.org/10.1007/s10114-025-3567-x

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Funding

Jun Liu is supported by the National Natural Science Foundation of China (Grant Nos. 12371102 and 12001527), the Natural Science Foundation of Jiangsu Province (Grant No. BK20200647) and the Postdoctoral Science Foundation of China (Grant No. 2021M693422)
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