共查询到20条相似文献,搜索用时 0 毫秒
1.
Chin-Cheng Lin 《分析论及其应用》2008,24(4):336-350
In this paper the classical Besov spaces Bsp.q and Triebel-Lizorkin spaces Fsp.q for s ∈R are generalized in an isotropy way with the smoothness weights {|2j|aln}∞j=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by Bap.q and Fap.q for a ∈Irk and k ∈N, respectively, keep many interesting properties, such as embedding theorems (with scales property for all smoothness weights), lifting properties for all parameters a, and duality for index 0 < p < ∞. By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between Bs,p.q and ∪tsBt,p.q,and between Fsp.q and ∪ts Ftp.q, respectively. Between Bs,p,q and ∪tsBt,p.qq,and between Fsp,qand ∪tsFtp.q,respectively. 相似文献
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The Herz type Besov and Triebel-Lizorkin spaces with variable exponent are introduced. Then characterizations of these new spaces by maximal functions are given. 相似文献
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We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case. 相似文献
4.
Yan Chang Han 《数学学报(英文版)》2009,25(11):1787-1804
In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for R^n. 相似文献
5.
JiangLiya XuMing 《高校应用数学学报(英文版)》2004,19(2):203-211
An equivalent definition of fractional integral on spaces of homogeneous type is given.The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed. 相似文献
6.
XU JingShi 《中国科学 数学(英文版)》2014,57(2):315-331
Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces by atoms,molecules and wavelets are given.These results generalize the corresponding results for classical Besov and Triebel-Lizorkin spaces. 相似文献
7.
Using the T1 theorem for the Besov and Triebel-Lizorkin spaces, we give new characterizations of Besov and Triebel-Lizorkin spaces with minimum regularity and cancellation conditions over spaces of homogeneous type. 相似文献
8.
Jingjing Fu 《Journal of Mathematical Analysis and Applications》2011,381(1):280-298
In this paper, Morrey type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Then equivalent quasi-norms of these new spaces in terms of Peetre?s maximal functions are obtained. Finally, applying those equivalent quasi-norms, the authors obtain the atomic, molecular and wavelet decompositions of these new spaces. 相似文献
9.
DENG Donggao & HAN Yongsheng Department of Mathematics Zhongshan University Guangzhou China Department of Mathematics Auburn University Alabama USA 《中国科学A辑(英文版)》2005,(5)
Using the discrete Calderon type reproducing formula and the Plancherel-Polya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved. 相似文献
10.
利用Clifford分析工具,给出了Lipschitz曲面上Besov空间与Triebel-Lizorkin空间定义,并研究其特征刻划. 相似文献
11.
We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin and Besov spaces. These include the , , potential, and Sobolev spaces. The main feature of our method is that the character of the basis functions can be prescribed in a very general way. In particular, if is any sufficiently smooth and rapidly decaying function, then our method constructs a basis whose elements are linear combinations of a fixed (small) number of shifts and dilates of the single function . Typical examples of such 's are the rational function and the Gaussian function This paper also shows how the new bases can be utilized in nonlinear approximation.
12.
Decomposition of Besov and Triebel-Lizorkin spaces on the sphere 总被引:1,自引:0,他引:1
A discrete system of almost exponentially localized elements (needlets) on the n-dimensional unit sphere Sn is constructed. It shown that the needlet system can be used for decomposition of Besov and Triebel-Lizorkin spaces on the sphere. As an application of Besov spaces on Sn, a Jackson estimate for nonlinear m-term approximation from the needlet system is obtained. 相似文献
13.
Using the discrete Calderon type reproducing formula and the PlancherelPolya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved. 相似文献
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A pair of dual frames with almost exponentially localized elements (needlets) are constructed on based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients. 相似文献
17.
Y.-S. Han 《Proceedings of the American Mathematical Society》1998,126(11):3315-3327
In this paper, using the discrete Calderon reproducing formula on spaces of homogeneous type obtained by the author, we obtain the Plancherel-Pôlya type inequalities on spaces of homogeneous type. These inequalities give new characterizations of the Besov spaces and the Triebel-Lizorkin spaces on spaces of homogeneous type introduced earlier by the author and E. T. Sawyer and also allow us to generalize these spaces to the case where . Moreover, using these inequalities, we can easily show that the Littlewood-Paley -function and -function are equivalent on spaces of homogeneous type, which gives a new characterization of the Hardy spaces on spaces of homogeneous type introduced by Macias and Segovia.
18.
This paper is concerned with the well-posedness of the Navier-Stokes-Nerst-Planck-Poisson system (NSNPP). Let sp=−2+n/p. We prove that the NSNPP has a unique local solution for in a subspace, i.e., Vu1×Vv1×Vv1, of with . We also prove that there exists a unique small global solution for any small initial data with . 相似文献
19.
YANG Dachun Department of Mathematics Beijing Normal University Beijing China 《中国科学A辑(英文版)》2005,48(1):12-39
Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|<(?) andmax{d/(d+(?)),d/(d+s+(?))}<q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p≤∞ and 0<q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|<(?),max{d/(d+(?)),d/(d+s+(?))}<p<∞ and max{d/(d+(?)),d/(d+s+(?))}<q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s=0 and q=2,thenH(?)_∞q~s(X)=(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)=BMO(X). 相似文献