A note on convolution-type Calderón-Zygmund operators

For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.     

Certain averaging operators on Triebel-Lizorkin spaces

Abstract. In this article, we study the boundedness properties of the averaging operator S_t^γon Triebel-Lizorkin spaces■ for various p, q. As an application, we obtain the norm convergence rate for S_t^γ(f ) on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_t^γis given.     

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.     

Boundedness of parabolic singular integrals and Marcinkiewicz integrals on Triebel-Lizorkin spaces

In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn).     

Triebel-Lizorkin空间和Besov空间上关于一类带Hardy核的振荡奇异积分

In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels.     

A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS

In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.     

Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters

Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderón's identity. This is inspired by the work of discrete Littlewood-Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe's covering lemma in multiparameter setting.     

Boundedness of an oscillating multiplier on Triebel-Lizorkin spaces

Abstract In this paper, we study Triebel-Lizorkin space estimates for an oscillating multiplier mΩ,α,β. This operator was initially studied by Wainger and by Fefferman-Stein in the Lebesgue spaces. We obtain the boundedness results on the Triebel-Lizorkin space Fpα,q（R^n） for different p, q.     

Commutators generated by multilinear Calderón-Zygmund type singular integral and Lipschitz functions

In this paper, we establish the boundedness of commutators generated by the multilinear Calderon- Zygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.     

奇异积分算子交换子在变指数空间上的特征

The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose, we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators. Immediately after, applying the characterizations of TriebelLizorkin space with variable exponent, we obtain that b ∈■β if and only if the commutator of Calderón-Zygmund singular integral operator is bounded, respectively, from■ to■,from■ to■ with■. Moreover, we prove that the commutator of Riesz potential operator also has corresponding results.     

一类关于波方程的振荡乘子在 Triebel-Lizorkin空间中的有界性

研究了与波方程的Cauchy问题相关的振荡乘子在Triebel-Lizorkin空间审F_p^γ,q（Rⁿ）中的有界性.     

卷积型Calder\'{o}n-Zygmund算子的新算法

Beylkin-Coifman-Rokhlin (B-C-R)算法表明算子通常可用$2n$维小波来分析, 而本文用 基于$n$维小波来引入一种新方法考虑卷积型 Calder\'{o}n-Zygmund (C-Z)算子. 利用此方法来研究算子的逼近, 此逼近算法不仅比 B-C-R 算法简单而且有更快的逼近速度. 还证明了 H\"{o}rmander 条件能够保证算子在 Besov 空间$\dot{B}_p^{0,q}\ (1\leq p,\, q \leq\infty)$ 和 Triebel--Lizorkin 空间$\dot{F}_p^{0,q}(1相似文献   

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q,L^p)^{\alpha}(\mathbf{R}^n)$ Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral $\mu_{\Omega,s}$ and Littlewood-Paley functions $\mu_{\Omega}$ and $\mu^{*}_{\lambda}$ on the weighted amalgam spaces $(L^{q}_\omega,L^{p})^{\alpha}(\mathbf{R}^{n})$ as $1 < q\leq \alpha < p\leq \infty$.     

与截面相关的Morrey空间与奇异积分

In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞.     

Triebel-Lizorkin Spaces of Para-Accretive Type and a Tb Theorem

In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type $\dot{F}^{\alpha,q}_{b,p}In this article, we use a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type , which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a necessary and sufficient condition for the boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with M _b TM _b ∈WBP is bounded from to if and only if and T ^* b=0 for , where ε is the regularity exponent of the kernel of T. Chin-Cheng Lin supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-008-021-MY3. Kunchuan Wang supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-259-009 and NCU Center for Mathematics and Theoretic Physics.     

Boundedness of Convolution-Type Operators on Certain Endpoint Triebel-Lizorkin Spaces

In this paper, we are concerned with the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. We establish the boundedness on [(F)\dot]₁^0,q\dot{F}_{1}^{0,q} (2<q<∞) under a very weak pointwise regularity condition. The boundedness is established by the Daubechies wavelets and the atomic-molecular approach.     

变指标Herz-Morrey空间上的Marcinkiewicz积分算子高阶交换子

In the case of Ω∈ Lipγ(Sn-1)(0 γ≤ 1), we prove the boundedness of the Marcinkiewicz integral operator μΩon the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators μmΩ,bwith b ∈ BMO(Rn) on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results.     

一类振荡积分算子在Wiener 共合空间上的有界性

假设a,b0并且K_(a,b)(x)=(e~(i|x|~(-b)))/(|x|~(n+a))定义强奇异卷积算子T如下:Tf(x)=(K_(a,b)*f)(x),本文主要考虑了如上定义的算子T在Wiener共合空间W(FL~p,L~q)(R~n)上的有界性.另一方面,设α,β0并且γ(t)=|t|~k或γ(t)=sgn(t)|t|~k.利用振荡积分估计,本文还研究了算子T_(α,β)f(x,y)=p.v∫_(-1)~1f(x-t,y-γ(t))(e~(2πi|t|~(-β)))/(t|t|~α)dt及其推广形式∧_(α,β)f(x,y,z)=∫_(Q~2)f(x-t,y-s,z-t~ks~j)e~(-2πit)~(-β_1_s-β_2)t~(-α_1-1)s~(-α_2-1)dtds在Wiener共合空间W(FL~p,L~q)上的映射性质.本文的结论足以表明,Wiener共合空间是Lebesgue空间的一个很好的替代.     

从Hardy空间到Zygmund-型空间的加权微分复合算子

设φ为单位圆盘D上的解析自映射,H(D)表示D上的所有解析函数的集合,u∈H(D).研究了从Hardy空间到Zygmund-型空间及小Zygmund-型空间的加权微分复合算子D_(φ,u)~n,的有界性和紧性,其中n∈N_0.