Besov spaces with variable smoothness and integrability on Lie groups of polynomial growth

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Abstract

In this paper, we consider the Besov spaces with variable smoothness and integrability on Lie groups of polynomial growth. We prove that such function spaces are well defined in the sense that their definitions are independent of the choice of basis functions under some specific assumptions. Then we show some embeddings related to them.

Keywords

Besov spaces Variable exponent Lie groups of polynomial growth Embedding 

Mathematics Subject Classification

42B25 43A80 46E30 

Notes

Acknowledgements

The authors would like to express great gratitude to the referees for the valuable comments and helpful suggestions.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Institution of Mathematics and Mathematical Education, School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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