加权Herz空间上交换子的有界性

旨在建立一大类由BMO函数和线性算子所生成交换了在另权Herz空间上的有界性,这些线性算子包括Calderon-Zygmund奇异积分算子,带有粗糙核的R.Fefferman型奇积分算子和带有粗糙核的Ricci-Stein-振荡奇异积分算子。     

一类粗糙奇异积分的加权 Triebel-Lizorkin有界性

本文研究了一类粗糙奇异积分算子的加权Triebel-Lizorkin有界性.对核函数Ω∈L log+L(Sn-1)建立了径向权函数的加权有界性;而对于核函数Ω∈Lr(Sn-1),1＜r≤∞,得到了一般的Muckenhopt权函数的加权有界性.     

ROUGH OPERATORS AND COMMUTATORS ON HOMOGENEOUS WEIGHTED HERZ SPACES

The authors esstablish the boundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions.In particular ,the Cadderon-Zygmund singular integrals and the rough R.Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.     

沿旋转曲面奇异积分的有界性

本文建立了具有粗糙核的沿曲面奇异积分算子的L^P有界性．其中粗糙核K(y)=Ω（y)/|y|^n,y∈R^n以及曲面{(y，φ(|y|）)：y∈R^n)满足某种光滑条件．同时，相应极大算子的有界性也被得到.     

各向异性极大算子及它们的应用

本文证明了一类与异性伸缩相关的极大算子在Ｌ＾ｐ（Ｒ＾ｎ）上是有界的，其中１〈ｐ≤∝，ｎ≥２。进一步，作为应用我们建立了算子Ｔｆ（ｘ）＝ｓｕｐε〉０│Ｔεｆ（ｘ）│Ｌ＾ｐ有界性，其中Ｔε是带有变化核的奇异积分。     

抛物型奇异积分算子在Triebel-Lizorkin空间的有界性

在Triebel-Lizorkin空间上建立了粗糙核抛物型奇异积分算子T的有界性,其中算子T定义为Tf(x)=p.v.∫_(Rn)(Ω(y))/(ρ(y)~β)f(x-y)dy,β≥n,ρ是伴随某种非迷向展缩的范数.     

一类次线性算子在广义Morrey空间上的加权有界性

本证明了如果次线性算子T在Orlicz空间上有介,则也有Morrey空间上有界,该算子包括极大算子和奇异积分算子等重要算子。     

L^p（R^n）BOUNDDNESS FOR THE MARCINKIEWICZ INTEGRAL

L^p(R^n)boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein.Some conditions implying the L^p(R^n) boundedness for the Marcinkiewicz integral are obtained.     

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ—TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Hertz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebrasin higher dimensions.     

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).     

Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces

In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel (x) satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.     

On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces

We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.     

Boundedness of rough oscillatory singular integral on Triebel-Lizorkin spaces

We give the boundedness on Triebel-Lizorkin spaces for oscillatory singular integral operators with polynomial phases and rough kernels of the form eiP(x)Ω(x)|x|⁻ⁿ, where Ω∈Llog⁺L(Sn−1) is homogeneous of degree zero and satisfies certain cancellation condition.     

Non-standard commutators for rough oscillatory singular integrals

In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 < p < ∞, the L ^p -boundedness of such operators are obtained provided that their kernels belong to the spaces L ^q (S ⁿ⁻¹) for some q > 1.     

一类振荡奇异积分算子在Triebel-Lizorkin空间的有界性

The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form ei|x|aΩ(x)|x|-n is studied,where a∈R,a≠0,1 and Ω∈L1(Sn-1) is homogeneous of degree zero and satisfies certain cancellation condition.When kernel Ω(x′)∈Llog L(Sn-1),the α,qp(Rn) boundedness of the above operator is obtained.Meanwhile,when Ω(x) satisfies L1-Dini condition,the above operator Tis bounded on 0,11(Rn).     

Certain oscillatory integrals on unit square and their applications

Let Q2 = [0, 1]2 be the unit square in two dimension Euclidean space R2. We study the Lp boundedness properties of the oscillatory integral operators Tα,β defined on the set S(R3) of Schwartz test functions f by Tα,βf(x,y,z) = Q2 f(x - t,y - s,z - tksj)e-it-β1s-β2t-1-α1s-1-α2dtds, where β1 > α1 0, β2 > α2 0 and (k, j) ∈ R2. As applications, we obtain some Lp boundedness results of rough singular integral operators on the product spaces.     

Multilinear singular and fractional integrals on weighted Hardy spaces

In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.