On a Class of Integral Operators

In this paper we consider the space where dv _s is the Gaussian probability measure. We give necessary and sufficient conditions for the boundedness of some classes of integral operators on these spaces. These operators are generalizations of the classical Bergman projection operator induced by kernel function of Fock spaces over .      

Lp Boundedness of Fourier Integral Operators in the Class S0,0

Acta Mathematica Sinica, English Series - We first prove the L2-boundedness of a Fourier integral operator where it’s symbol $$a in S_{{1 over 2},{1 over 2}}^0left( {{mathbb{R}^n} times...     

Boundedness and Compactness of Operators on the Fock Space

We obtain sufficient conditions for a densely-defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.     

On the Boundedness of Singular Integral Operators in Symmetric Spaces

We consider the integral convolution operators \varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}$$ " align="middle" border="0"> defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we establish necessary and sufficient conditions under which the operators {T } are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces.     

Boundednes of Singular Integral Operators On Some Atom Spaces

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Net Spaces and Boundedness of Integral Operators

In this paper we introduce new functional spaces which we call net spaces. Using their properties, necessary and sufficient conditions for the integral operators to be of strong or weak type are obtained. Estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.     

Criteria for the Boundedness and Compactness of Operators with Power-Logarithmic Kernels

In the present work, necessary and sufficient conditions are given in terms of a nonnegative Borel measure which ensure the boundedness and compactness of operators with power-logarithmic kernels from L ^p (0, a) to L ^p (0, a) (or to L ^q (0, a)), where 0 < a < , 1 < p, q < , > 1/p and 0.     

Boundedness, Compactness and Schatten-class Membership of Weighted Composition Operators

The boundedness and compactness of weighted composition operators on the Hardy space H²{{\mathcal H}^2} of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces A²_a(\mathbbD){\mathcal{A}^2_\alpha(\mathbb{D})} are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.     

On the Compactness and Approximation Numbers of Hardy-Type Integral Operators in Lorentz Spaces

We characterize the mapping properties such as the boundedness,compactness and measure of noncompactness for those real weightfunctions , , u0, v0, for which the Hardy-type integral operatorof the form acts from to , when the parameters are restricted to the range 1 < max (r,s) min (p, q) < and the kernel k(x, y) 0 satisfies theOinarov condition (see (2) below). For the case k(x, y) = 1,we obtain lower and upper estimates of the approximation numbers,extending the result of [5].     

一类多线性积分算子的端点有界性

本文对一类相关于非卷积型算子的多线性算子,证明了其在端点情形上的有界性,该算子包括Littlewood-Paley算子和Marcinkiewicz算子．     

Weighted Boundedness for a Class of Rough Multilinear Operators

In this paper we give the (L ^p (ω ^p ), L ^q (ω ^q )) boundedness for a class of multilinear operators, which is simular to the higher-order commutator for the rough fractional integral. In our results the kernel function is merely assumed on a size condition. Received August 21, 2000, Accepted October 24, 2000     

The Boundedness of Two Classes of Integral Operators

Czechoslovak Mathematical Journal - The aim of this paper is to characterize the Lp ? Lq boundedness of two classes of integral operators from Lp( $${\cal U}$$ , dVα) to Lq( $${\cal U}$$...     

多线性分数次积分算子交换子的有界性

本文利用sharp极大函数的估计,证明了一类由多线性分数次积分算子和BMO(Rn)函数生成的交换子的Lp(Rn)有界性.     

一类再生Hilbert空间上偏微分算子的有界性(英文)

研究了一类再生Hilbert空间上偏微分算子的有界性,得到了偏微分算子有界的一个充分必要条件,推广了文献[1]中的结果.     

一类再生Hilbert空间上偏微分算子的有界性

研究了一类再生Hilbert空间上偏微分算子的有界性,得到了偏微分算子有界的一个充分必要条件,推广了文献中的结果．     

一类奇异积分算子在Banach空间值Hardy空间上的有界性

该文绘出了一类卷积型奇异积分算子在Banach空间值Hardy空间H（Rn）上的有界性．     

On Some Structural Properties of Banach Function Spaces and Boundedness of Certain Integral Operators

In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair (X, Y) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from X into Y of the form

齐次群上多线性奇异积分算子的有界性

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.