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A q-Atomic Decomposition of Weighted Tent Spaces on Spaces of Homogeneous Type and Its Application

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Abstract

The theory of tent spaces on \({\mathbb {R}}^n\) was introduced by Coifman, Meyer and Stein, including atomic decomposition, duality theory and so on. Russ generalized the atomic decomposition for tent spaces to the case of spaces of homogeneous type \((X,d,\mu )\). The main purpose of this paper is to extend the results of Coifman, Meyer, Stein and Russ to weighted version. More precisely, we obtain a q-atomic decomposition for the weighted tent spaces \(T^p_{2,w}(X)\), where \(0<p\le 1, 1<q<\infty ,\) and \(w\in A_\infty \). As an application, we give an atomic decomposition for weighted Hardy spaces associated to non-negative self-adjoint operators on X.

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Notes

  1. There are also some other weighted tent spaces which are different from that of our paper. See, for example, [2, 37]

  2. The case \(\mu (X) < {\infty } \) is rather different, some techniques and results in this article may be failure; see [9].

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Acknowledgements

We would like to thank the referee for valuable comments and suggestions. We also thank Lixin Yan for helpful discussions. L. Song is supported by NNSF of China (Grant No. 11622113) and NSF for distinguished Young Scholar of Guangdong Province (Grant No. 2016A030306040).

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  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Liang Song & Liangchuan Wu

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  1. Liang Song
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Song, L., Wu, L. A q-Atomic Decomposition of Weighted Tent Spaces on Spaces of Homogeneous Type and Its Application. J Geom Anal 31, 3029–3059 (2021). https://doi.org/10.1007/s12220-020-00382-6

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