Boundedness of generalized fractional integral operators

The authors introduce a new kind of fractional integral operators, namely, the so called (θ,N)-type fractional integral operators, and discuss their boundedness on the Hardy spaces, the weak Hardy spaces and the Herz-type Hardy spaces.     

The boundedness of bilinear singular integral operators on Sierpinski gaskets

In the paper we give the boundedness estimate of bilinear singular integral operators on Sierpinski gasket inspired from [1].     

WEAK TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATORS ON GENERALIZED NON-HOMOGENEOUS MORREY SPACES

We obtain weak type (1,q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces.The proofs use some properties of maximal operators.Our results are closely related to the strong type inequalities in [13,14,15].     

Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^˙α(?)_p(?,q(?)),such as some sublinear operators,the fractional integral and its commutator.     

Bounds for commutators of multilinear fractional integral operators with homogeneous kernels

We will show bounds for commutators of multilinear fractional integral operators with some homogeneous kernels.     

The boundedness of Toeplitz-type Operators on vanishing-morrey spaces

In this note,we prove that the Toeplitz-type Operator Θ b α generated by the generalized fractional integral,Calderón-Zygmund operator and VMO funtion is bounded from L p,λ (R n) to L q,μ (R n).We also show that under some conditions Θαb f ∈ V L q,μ (B R),the vanishing-Morrey space.     

THE BOUNDEDNESS FOR A CLASS OF ROUGH FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT LEBESGUE SPACES

In this paper,we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from L p 1 (·) (R n) to L p 2 (·) (R n).     

有变量核的分数次积分算子交换子的CBMO估计(英文)

In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.     

WEIGHTED BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL HARDY OPERATORS WITH BESOV-LIPSCHITZ FUNCTIONS

In this paper,we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions.The main result is that this kind of commutator,denoted by Hb α,is bounded from L x γp (R +) to Lx δ q (R +) with the bound explicitly worked out.     

BOUNDEDNESS FOR THE COMMUTATOR OF FRACTIONAL INTEGRAL ON GENERALIZED MORREY SPACE IN NONHOMOGENEOUS SPACE

In this paper,we will establish the boundedness of the commutator generated by fractional integral operator and RBMO(μ) function on generalized Morrey space in the non-homogeneous space.     

Boundedness of fractional integral operators in Herz-type spaces on locally compact Vilenkin groups

Let G be a locally compact Vilenkin group. In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaceson G are obtained.     

Sharp constants for a class of multilinear integral operators and some applications

We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.     

A CHARACTERIZATION FOR FRACTIONAL INTEGRALS ON GENERALIZED MORREY SPACES

This paper concerns with the fractional integrals,which are also known as the Riesz potentials.A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be presented.Our results can be viewed as a refinement of Nakai’s [7].     

SOME GENERALIZATIONS ON THE BOUNDEDNESS OF BILINEAR OPERATORS

For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.     

Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

Let T be the singular integral operator with variable kernel, T*be the adjoint of T and T~#be the pseudo-adjoint of T. Let T_1T_2 be the product of T_1 and T_2, T_1? T_2 be the pseudo product of T_1 and T_2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator Dγon the weighted Morrey spaces.     

WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.     

Modulation space estimates for the fractional integral operators

We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.     

ALMOST AUTOMORPHIC MILD SOLUTIONS TO SOME FRACTIONAL DELAY DIFFERENTIAL EQUATIONS

In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.     

New Criterion for Starlike Integral Operators

In this paper, we introduce new sufficient conditions for certain integral operators to be starlike and p-valently starlike in the open unit disk.     

Bilinear pseudo-differential operators on local hardy spaces

In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Ho¨rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.