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).     

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.     

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL,Ⅱ

Let n≥2. In this paper, the author establishes the L^2 (R^n)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hypergeometric functions and congqucnt hypergeometric funtions.     

Rough multiple singular integrals along hypersurfaces

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm-1 × Sn-1) (ε = 1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.     

On Multiple Singular Integrals along Polynomial Curves with Rough Kernels

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.     

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.     

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.     

Maximal operators and singular integrals with non-isotropic dilation on product domains

In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L（logL）a（E1 × E2） for some a 〉 0, which is optimal.     

Multilinear singular integrals and commutators in variable exponent Lebesgue spaces

Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.     

A new class of weights adapted to rough singular integrals and Marcinkiewicz integrals

In this paper, we introduce a new class of weights Ap （Rn） which retains many fine properties of the classical Muchenhoupt weights Ap （Rn）. While Ap （Rn） is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class Ap （Rn） adapts well to these rough operators. As applications, we improve some known weighted estimates.     

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）.     

The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent

The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.     

Rough singular integrals associated to surfaces of revolution

Let and . The authors establish the -boundedness for a class of singular integral operators associated to surfaces of revolution, , with rough kernels, provided that the corresponding maximal function along the plane curve is bounded on .

     

Commutators of weighted lipschitz functions and multilinear singular integrals with non-smooth kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.     

Rough singular integrals on Triebel–Lizorkin space and Besov space

In this paper the authors prove that the homogeneous singular integral T_Ω with ΩH¹(Sⁿ⁻¹) is bounded on the Triebel–Lizorkin spaces and the Besov spaces. These results answer an open problem proposed by Chen and Zhang in [J. Chen, C. Zhang, Boundedness of rough singular integral on the Triebel–Lizorkin spaces, J. Math. Anal. Appl. 337 (2008) 1048–1052]. The same results hold also for the rough singular integral operators T_Ω,h with radial function kernels.     

Applications of some block spaces to singular integrals

This paper is a survey on the theory and application of some block spaces on the unit sphere introduced by Jiang and the author of this paper in the study of singular integrals and some related operators with rough kernels.      

Bmo boundedness for banach space valued singular integrals

In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved.     

A criterion on weighted boundedness for rough multilinear oscillatory singular integrals

In this paper the authors give a criterion on the weighted boundedness of the multilinear oscillatory singular integral operators with rough kernels.

     

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.