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).     

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].     

A NOTE ON MARCINKIEWICZ INTEGRALS WITH H^1 KERNELS

This paper shows that for Ω∈ H1(Sn-1), Marcinkiewicz integral operator μΩ is Lp(Rn) bounded for 1 < p <∞, which improves some known results.     

区域上Triebel-Lizorkin空间的原子分解与限制定理

本文在区域Ω( Rn,n≥1)上定义了某类在边界上消失的Triebel-Lizorkin空间 ,并给出了它的原子分解定理,对偶定理.同时证明了当区域 时,得到了限制和扩张定理     

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 (x) where P(x,y) is a nontrivial and real-valued polynomial defined on Rn × Rn, Ω(x) is homogeneous of degree zero on Rn, 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=∑rs=1ms, the author proves that if 0<β=∑rs=1βs<1, and Ω∈ Lq(Sn-1) for some q ＞ 1/(1 - β), then for any p ∈ (1, ∞), and some appropriate 0 ＜ β ＜ 1, TA1,A2,…,Ar is bounded on Lp(Rn).     

Clifford分析中奇异积分的反转公式

借助于多元复分析的思想,本文用两种方法证明了Clifford分析中奇异积分的反转公式．     

具广义Calderón-Zygmund核的多线性振荡奇异积分极大算子的有界性

本文研究了具有广义Calderon-Zygmund核的多线性奇异积分极大算子和多线性振荡奇异积分极 大算子,证明了这类极大算子的Lp-有界性．     

乘积空间上粗糙Marcinkiewicz积分算子的一点注记

本文将证明:对于,以及,积域上Marcinkiewicz积分算子为有界,其中1相似文献   

Triebel-Lizorkin空间和Besov空间上关于一类带Hardy核的振荡奇异积分

In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels.     

有界对称域上混合范数空间的乘子变换

本文考虑了Ｃ＾ｎ中有界对称域Ω上的混合范数空间Ｈｐ，ｑ，ａ（Ω）它包含许多重要的函数空间，如Ｈａｒｄｙ空间、Ｂｅｒｇｍａｎ空间、缓慢增长的函数空间以及Ｂｐｑ，研究了Ｈｐ，ｑ，ａ（Ω）中函数的现人类 乘子变 得到了Ｈｐ，ｑ，ａ（Ω）中的Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ定理。这些结果均推了以前一系列结论。     

A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R~n

The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight Wλ(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.     

THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS

Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.     

Banach空间中非光滑指标奇异最优控制

本文对于Ｂａｎａｃｈ空间中分布参数系统讨论非光滑指标奇异最优控制问题，利用Ｍｏｏｒｓ－Ｐｅｎｒｏｓｅ广义逆与Ｃｌａｒｋｅ广义梯度证得奇异最优控制的存在性，并给出广义一阶必要条件，推广了Ｌｉｏｎｓ［３］的相应结果．     

实Clifford分析中六类拟Bochner-Martinelli型高阶奇异积分的几个问题

本文借助于Ｈａｄａｍａｒｄ关于高阶奇异积分有限部分的思想,研究关于实 Ｃｌｉｆｆｏｒｄ分析中六个类型(含一个奇点或二个奇点的)拟Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ型高阶奇异积分的归纳定义、Ｈａｄａｍａｒｄ主值的存在性、递推公式、计算公式、微分公式、Ｐｏｉｎｃａｒｅ－Ｂｅｒｔｒａｎｄ置换公式以及拟Ｂ－Ｍ型高阶奇异积分的Ｈｏｌｄｅｒ连续性等问题．这些问题是研究单、多元复分析的学者们在研究奇异积分时,通常要涉及到的几个问题．     

ON THE MIXED PROBLEMS IN AN EIASTIC PIANE WITH PERIODIC CRACKS

ＯＮＴＨＥＭＩＸＥＤＰＲＯＢＬＥＭＳＩＮＡＮＥＩＡＳＴＩＣＰＩＡＮＥＷＩＴＨＰＥＲ１ＯＤＩＣＣＲＡＣＫＳＺｈｅｎｇＫｅ（郑可）（ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ）ＯＮＴＨＥＭＩＸＥＤＰＲＯＢＬＥＭＳＩＮＡＮＥＩＡＳＴＩＣＰＩＡＮＥＷＩＴＨＰＥＲ１ＯＤＩ...     

实轴上几种高阶奇异积分的换序公式

给出实轴上几种类型高阶奇异积分的换序公式,由于∞点的特异性,对公式（４）,（９）尤加特别注意。     

MULTIPLICITY OF NONNEGATIVE SOLUTIONS TO SECOND-ORDER SINGULAR DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS IN BANACH SPACES

This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].     

关于变化再生核希尔伯特空间在线算法的一个注记

本文研究了由高斯核的方差在算法中引起的一些误差,利用再生核的一些特殊性质对这些误差进行分析.这些误差在分析算法的收敛速度时起到了重要的作用.     

A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.