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Intrinsic atomic characterization of 2-microlocal spaces with variable exponents on domains

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Abstract

We provide an intrinsic atomic characterization for 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability on domains, \(B_{p(\cdot ),q(\cdot )}^{\varvec{w}}(\varOmega )\) and \(F_{p(\cdot ),q(\cdot )}^{\varvec{w}}(\varOmega )\), where \(\varOmega \) is a regular domain. We make use of the non-smooth atomic decomposition result obtained in Gonçalves and Kempka (J Math Anal Appl 434:1875–1890, 2016) for these spaces to get the main result.

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Acknowledgements

We would like to thank the anonymous referee for the valuable suggestions, which helped us to improve the content of this work. Especially, the philosophical question raised in Remark 4 is based on comments of the referee. Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. KE 1847/1-2).

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Authors and Affiliations

  1. Faculty of Mathematics, TU Chemnitz, Reichenhainer Str. 39, 09126, Chemnitz, Germany

    Helena F. Gonçalves & Henning Kempka

  2. Department of Fundamental Sciences, University of Applied Sciences, PF 100314, 07703, Jena, Germany

    Helena F. Gonçalves & Henning Kempka

Authors
  1. Helena F. Gonçalves
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  2. Henning Kempka
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Correspondence to Helena F. Gonçalves.

Additional information

The authors were supported by the German science foundation (DFG) within the Project KE 1847/1-2.

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Gonçalves, H.F., Kempka, H. Intrinsic atomic characterization of 2-microlocal spaces with variable exponents on domains. Rev Mat Complut 30, 467–486 (2017). https://doi.org/10.1007/s13163-017-0231-8

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