SURVEY ARTICLE

Applications of multiresolution analysis in Besov-Q type spaces and Triebel-Lizorkin-Q type spaces

  • Pengtao LI , 1 ,
  • Wenchang SUN 2
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  • 1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
  • 2. School of Mathematical Sciences, Nankai University, Tianjin 300000, China

Published date: 15 Jun 2022

Copyright

2022 Higher Education Press

Abstract

In this survey, we give a neat summary of the applications of the multi-resolution analysis to the studies of Besov-Q type spaces B ˙ p,q γ1,γ2(n) and Triebel-Lizorkin-Q type spaces B˙p, qγ1, γ2( n). We will state briefly the recent progress on the wavelet characterizations, the boundedness of Calderón-Zygmund operators, the boundary value problem of B ˙ p,q γ1,γ2(n) and F ˙ p,q γ1,γ2(n). We also present the recent developments on the well-posedness of fluid equations with small data in B˙p, qγ1, γ2( n) and F ˙p ,qγ1,γ2( n).

Cite this article

Pengtao LI , Wenchang SUN . Applications of multiresolution analysis in Besov-Q type spaces and Triebel-Lizorkin-Q type spaces[J]. Frontiers of Mathematics in China, 2022 , 17(3) : 373 -435 . DOI: 10.1007/s11464-022-1015-0

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