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) (R^(n))and Triebel-Lizorkin-Q type spaces B_(p,q)^(γ1,γ2) (R^(n)).We...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) (R^(n))and Triebel-Lizorkin-Q type spaces B_(p,q)^(γ1,γ2) (R^(n)).We will state briefly the recent progress on the wavelet characterizations,the boundedness of Calderon-Zygmund operators,the boundary value problem of B_(p,q)^(γ1,γ2) (R^(n)) and F_(p,q)^(γ1,γ2) (R^(n)).We also present the recent developments on the well-posedness of fluid equations with small data in B_(p,q)^(γ1,γ2) (R^(n))and F_(p,q)^(γ1,γ2) (R^(n)).展开更多
The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+&...The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+</sub>). Our approach is based on the M-boundedness of linear operators B<sup>s</sup><sub>p,q</sub>-multipliers and some results in Besov space.展开更多
Abstract With the help of the maximal function caracterizations of the Besov-type space Bs,τp,q and the TriebelLizorkin-type space Fs,τp,q,we present the atomic decomposition of these function spaces.Our results cov...Abstract With the help of the maximal function caracterizations of the Besov-type space Bs,τp,q and the TriebelLizorkin-type space Fs,τp,q,we present the atomic decomposition of these function spaces.Our results cover the results on classical Besov and Triebel-Lizorkin spaces by taking τ=0.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11171203,11201280)Specialized Research Fund for the Doctoral Program of Higher Education of China(No.2011440212003).
文摘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) (R^(n))and Triebel-Lizorkin-Q type spaces B_(p,q)^(γ1,γ2) (R^(n)).We will state briefly the recent progress on the wavelet characterizations,the boundedness of Calderon-Zygmund operators,the boundary value problem of B_(p,q)^(γ1,γ2) (R^(n)) and F_(p,q)^(γ1,γ2) (R^(n)).We also present the recent developments on the well-posedness of fluid equations with small data in B_(p,q)^(γ1,γ2) (R^(n))and F_(p,q)^(γ1,γ2) (R^(n)).
文摘The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+</sub>). Our approach is based on the M-boundedness of linear operators B<sup>s</sup><sub>p,q</sub>-multipliers and some results in Besov space.
文摘Abstract With the help of the maximal function caracterizations of the Besov-type space Bs,τp,q and the TriebelLizorkin-type space Fs,τp,q,we present the atomic decomposition of these function spaces.Our results cover the results on classical Besov and Triebel-Lizorkin spaces by taking τ=0.
