Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces

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.     

Singular integrals on the discrete Besov space B1 0,1 (Z)

Summary We show the boundedness of singular integral operators on the discrete Besov space B₁^0,1 (Z). For this purpose, we introduce discrete special molecules on B₁^0,1 (Z).     

区域上Besov空间的分子分解及其在偏微分方程中的应用

该文先刻划了外正则区域ΩR^n(n≥1)上Besov空间B^{s,p}_p(s<0,0相似文献   

Besov空间和Zygmund空间上的复合算子

讨论单位圆盘上Besov空间B（p,q）和Zygmund空间Z及小Zygmund空间Z_0之间的复合算子,得到了B（p,q）到Z（Z_0）的复合算子以及Z（Z0）到B（p,q）的复合算子有界或紧的充要条件。     

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.     

Interpolating Sequences for Besov Spaces

We characterise the interpolating sequences for the Besov spaces B_p and for their multiplier spaces. We also construct linear operators of interpolation.     

赋以混合范数的各向异性Besov类在不同度量下的嵌入定理

本文给出了赋以混合范数的各向异性多元Besov类BPθr(Rd)的一个表现定理, 利用此表现定理,证明了它在不同度量下的一个嵌入定理BPθr(Rd)→Bqθr'(Rd),其中 1≤P≤q≤∞,r'=(1-∑jd=1(1/pj-1/qj)1/rj)r．     

Lipschitz曲面上的Besov空间和Triebel-Lizorkin空间

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．     

Generalized Besov spaces and Triebel-Lizorkin spaces

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.     

Lipschitz Invariance of Critical Exponents on Besov Spaces

In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.     

关于Szász-Mirakjan—Durrmeyer算子在Besov空间上的逼近阶

本文主要给出了Ｓｚａｓｚ－Ｍｉｒａｋｊａｎ－Ｄｕｒｒｍｅｙｅｒ算子在Ｂｅｓｏｖ空间上逼近阶的特征刻划     

Herz型Besov和Triebel-Lizorkin空间的原子分解

该文给出了Herz型Besov和Triebel-Lizorkin空间的原子分解.     

单位球上Besov空间的Toeplitz算子

考虑了全纯Besov空间B_p上的Toeplitz算子T_μ~α,这里μ是单位球上的一个复Borel测度.给出了T_μ~α在B_p上有界的一些充要条件.     

Point-wise Multipliers of Herz-type Besov Spaces and Their Applications

In this paper, the point-wise multipliers for the Herz-type Besov spaces are obtained, and the pseudo-differential operators are proved to be bounded in the Herz-type Besov spaces by using the point-wise multipliers. This paper was selected from Math. Appl., 2004, 17(1), 115–121     

单位球上Bergman空间到Besov空间的广义Cesaro算子(英文)

本文利用Carleson测度刻画了Bergman空间到Besov空间的广义Cesaro算子T_g的有界性和紧性,同时得到了(p,q)-φCarleson测度的一些性质.     

Herz型Besov空间的点态乘子及应用

作者研究了Herz型Besov空间的点态乘子 ,并利用此点态乘子证明了一类拟微分算子在Herz型Besov空间上的有界性     

On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm

In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.     

d-集上的Besov空间的一个迹定理

In the paper we give a trace theorem of Besov spaces Bαp,p(Rn) on a d-set.It is a kind of extension of related results of Jonsson and Wallin,which has important applications on PDE theory.     

Commutators for Fourier multipliers on Besov Spaces

If T is any bounded linear operator on Besov spaces B_p^σ_j,q_j(Rⁿ)(j=0,1, and 0<σ₁<σ<σ₀), it is proved that the commutator [T,T_μ]=TT_μ−T_μT is bounded on B_p^σ,q(Rⁿ), if T_μ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas.