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Triebel–Lizorkin spaces with variable smoothness and integrability on Lie groups of polynomial growth

  • Jingxuan Fang
  • Jiman Zhao
Article
  • 86 Downloads

Abstract

In this paper we characterize Triebel–Lizorkin spaces \(F_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}\) with variable smoothness and integrability on Lie groups of polynomial growth. We show that such spaces can be well defined under some conditions. By molecular decomposition we give the relationship between the spaces \(F_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}\) and \(f_{p(\cdot ),q(\cdot )}^{\alpha (\cdot )}\).

Keywords

Triebel–Lizorkin spaces Variable exponent Lie groups of polynomial growth Molecular decomposition 

Mathematics Subject Classification

42B25 43A80 46E30 

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Copyright information

© Springer International Publishing AG 2017

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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