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Variable 2-Microlocal Besov–Triebel–Lizorkin-Type Spaces

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Abstract

This article is devoted to the study of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of ϕ-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some related Sobolev-type embeddings and trace theorems of these spaces are also established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel–Lizorkin spaces.

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Authors and Affiliations

  1. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Su Qing Wu, Da Chun Yang & Wen Yuan

  2. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hu’nan Normal University, Changsha, 410081, P. R. China

    Ci Qiang Zhuo

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  1. Su Qing Wu
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  2. Da Chun Yang
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Correspondence to Wen Yuan.

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Wu, S.Q., Yang, D.C., Yuan, W. et al. Variable 2-Microlocal Besov–Triebel–Lizorkin-Type Spaces. Acta. Math. Sin.-English Ser. 34, 699–748 (2018). https://doi.org/10.1007/s10114-018-7311-7

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