Variation Inequalities for the Commutators of One-Sided Calderón-Zygmund Singular Integrals with Lipschitz Functions

In this paper, we establish the weighted Lp (1 < p < ∞) boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.

Weighted L^p-boundedness of Multilinear Oscillatory Singular Integrals with Calderón-Zygmund Kernel

In this paper, weighted L p-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.

A LIPSCHITZ ESTIMATE FOR MULTILINEAR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS

In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.

A CLASS OF OSCILLATORY SINGULAR INTEGRALS ON TRIEBEL-LIZORKIN SPACES

The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.

WEIGHTED ESTIMATE FOR THE MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATORS

In this paper, the weighted Lp(Rn) boundedness for the multilinear oscillatory singular integral operators with polynomial phases is studied.

L^2(R^n) BOUNDEDNESS FOR COMMUTATORS OF OSCILLATORY SINGULAR INTEGRAL OPERATORS

The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).

A SURVEY ON OSCILLATORY INTEGRAL OPERATORS

This is a short survey on osicllatory integral operators. We summarize the main development and managing techniques of the field, and give some open problems and main references in the end.

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL, Ⅱ

Let n≥2. In this paper, the author establishes the L2 (Rx)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hyper geometric functions and confluent hyper geometric funtions.

NON-CONVOLUTION TYPE OSCILLATORY SINGULAR INTEGRAL ON HARDY SPACE HK_p(R^n)

The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.

BOUNDEDNESS OF OSCILLATORY SINGULAR INTEGRALS ON HK_P SPACES

In this paper, we consider the HK boundedness for certain oscillatory singular integral operators.

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.

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 Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.

Oscillatory Strongly Singular Integral Associated to the Convex Surfaces of Revolution

Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.

A WEIGHTED NORM INEQUALITY FOR THETA(t)-TYPE OSCILLATORY SINGULAR INTEGRALS

The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.

Boundedness of Multilinear Oscillatory Singular Integral on Weighted Weak Hardy Spaces

In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.

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.

Boundedness of a Kind of Oscillatory Singular Integral Operators

In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^n）（1〈p〈∞） when -1〈u〈 αd（1/2-｜1/p-1/2）.

integral from n=a to b (f(x)sin) mxdx类高振荡积分计算的一种方法

本文提出利用样条函数计算高振荡积分,克服了高次插值的严重缺点,同时避免了利用分步积分需要计算的函数在区间端点处的高阶导数,能大幅度提高计算的精确度。

A SHARP FUNCTION ESTIMATE FOR MULTILINEAR SINGULAR INTEGRAL OPERATORS

A variant sharp function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given.

Boundedness of singular integrals along surfaces on Lebesgue spaces

In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.