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Analysis and Mathematical Physics

, Volume 9, Issue 4, pp 2385–2411 | Cite as

Characterizations of even-order Musielak–Orlicz–Sobolev spaces via ball averages and their derivatives

  • Tao MaEmail author
  • Zhenyu Yang
Article
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Abstract

In this paper, the authors present some new characterizations of the Musielak–Orlicz–Sobolev spaces with even smoothness order via ball averages and their derivatives on the radius. Consequently, as special examples of the Musielak–Orlicz–Sobolev spaces studied in this paper, the corresponding characterizations for some weighted Sobolev spaces, Orlicz–Sobolev spaces and variable Sobolev spaces are also obtained. Since these characterizations depend only on ball averages and their derivatives on the radius, they provide some possible ways to introduce the corresponding function spaces on any metric measure space.

Keywords

Sobolev space Orlicz space Musielak–Orlicz space Ball average 

Mathematics Subject Classification

Primary 46E35 Secondary 42B25 42B35 
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Notes

Acknowledgements

The authors would like to thank the anonymous referees for their carefully reading and many useful corrections which do improve the presentation of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China

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