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1.
本文用新的方法研究B-M型积分的边界性质,所得结果推进了文[1]的结果,并指出文[4]证明有错误  相似文献   

2.
闭逐块光滑流形上的Cauchy—Fantanppie型积分的边界性质   总被引:9,自引:0,他引:9  
林良裕 《数学学报》1995,38(1):13-23
对C^n空间中具有逐块C^(1)光滑可定向边界δD的有界域D和著名的Cauchy-Fantappie公式,本文定义一类与Bochner-martinelli核同伦等价的C-F核Ω,应用同伦方法证明具有Holder密度的相应奇异积分F(t)存在哥西主值和C-F型积分F(z)存在满足Holder条件的内,外极限值F^+(t)和F^-(t);同时建立一个更一般的含有边界上点t的立体角系数α(t)的Ple  相似文献   

3.
对C ̄n空间中具有逐块C ̄(1)光滑可定向边界D的有界域D和著名的Cauchy-Fantappie公式,本文定义一类与Bochner-Martinelli核同伦等价的C-F核Ω,应用同伦方法证明具有Holder密度的相应奇异积分F(t)存在哥西主值和C-F型积分F(z)存在满足Holder条件的内、外极限值F ̄+(t)和F ̄-(t);同时建立一个更一般的含有边界上点t的立体角系数α(t)的Plemelj公式。  相似文献   

4.
关于Bochner-Martinelli积分边界性质的研究,前人已有许多结果,在边界是C1光滑核密度函数是Holder连续的条件下本文给出了Plemelj公式的一个简单证法,并且极限是任意的而不仅是法向极限或沿角区域的极限.  相似文献   

5.
关于多复变数某些积分表示式的剖析   总被引:1,自引:0,他引:1       下载免费PDF全文
  相似文献   

6.
关于多复变数积分表示的注释   总被引:1,自引:0,他引:1  
近年来许多文章应用所谓的A类函数来建立C空间中有界域上的积分表示.本文证明了C(n≥2)中任意一有界域上根本不存在这种A类函数,并指出目前多复变数积分表示中存在的一些模糊概念和本质的错误  相似文献   

7.
实Clifford分析中的拟Bochner Martinelli型高阶奇异 积分   总被引:1,自引:0,他引:1       下载免费PDF全文
该文借助于高阶奇异积分的Hadmard主值思想以及归纳法思想讨论了实Clifford分析中拟Bochner Martinelli型高阶奇异积分Hadmard主值的存在性、递推公式、计算公式,以及在Hadamard主值意义下的微分公式.  相似文献   

8.
T_b表示由加权Lipschitz函数b与Calderon-Zygmund奇异积分算子T生成的交换子.研究了T_b在加权Herz型Hardy空间上的有界性质,并在端点处证明了交换子是从加权Herz型Hardy空间到加权弱Herz空间的有界算子.  相似文献   

9.
胡越  王月山  王艳烩 《数学杂志》2015,35(2):443-450
本文研究了由分数次积分I_l与加权Lipschitz函数b生成的交换子[b,I_l]在加权Herz型Hardy空间上的估计.利用加权Herz型Hardy空间的分解理论,得到了交换子[b,I_l]从加权Herz型Hardy空间到(弱)加权Herz空间上的有界性质.  相似文献   

10.
本文给出具分光滑边界Ω的域D包含C^n上的Cauchy-Fantappie型积分表示的内外极限值:Φ^ (t)=(1-β(t)/S)ψ(t) ∫Ω^ψ(ξ)K(ξ,t) Φ^-(t)=(-β(t)/S)ψ(t) ∫Ω^ψ(ξ)K(ξ,t)属于H(α,Ω),推广了陈叔谨先生1994年得到的一个结果。  相似文献   

11.
An equivalent definition of fractional integral on spaces of homogeneous type is given.The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.  相似文献   

12.
On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Hlder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Hlder continuous property on the boundary.  相似文献   

13.
In this paper, we discuss several classes of convolution type singular integral equations with variable integral limits in class $ H^*_1 $. By means of the theory of complex analysis, Fourier analysis and integral transforms, we can transform singular integral equations with variable integral limits into the Riemann boundary value problems with discontinuous coefficients. Under the solvability conditions, the existence and uniqueness of the general solutions can be obtained. Further, we analyze the asymptotic properties of the solutions at the nodes. Our work improves the Noether theory of singular integral equations and boundary value problems, and develops the knowledge architecture of complex analysis.  相似文献   

14.
In the present paper we state some approximation theorems concerning pointwise convergence and its rate for a class of non-convolution type nonlinear integral operators of the form:Tλ (f;x) = B A Kλ (t,x, f (t))dt , x ∈< a,b >, λ∈Λ. In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 of f as (x,λ ) → (x0,λ0) in L1 < A,B >, where < a,b > and < A,B > are is an arbitrary intervals in R, Λ is a non-empty set of indices with a topology and λ0 an accumulation point of Λ in this topology. The results of the present paper generalize several ones obtained previously in the papers [19]-[23].  相似文献   

15.
The higher spin operator of several R6 variables is an analogue of the ■-operator in theory of several complex variables.The higher spin representation of so6(C)is ⊙kC4 and the higher spin operator Dk acts on ⊙kC4-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R6variables.The embedding of R6n into the space of co...  相似文献   

16.
The solution of an initial‐boundary value problem for bending of a piecewise‐homogeneous thermoelastic plate with transverse shear deformation is represented as various combinations of single‐layer and double‐layer time‐dependent potentials. The unique solvability of the boundary integral equations generated by these representations is proved in spaces of distributions. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

17.
The boundary integral equation formulation of thermoelasticity problems from part I is applied to crack problems in both finite and infinite thermoelastic bodies. For a flat crack in an infinite body the normal and tangential crack opening displacement are decoupled. Transient and steady state problems of thermoelasticity, as well as stationary problems, are considered.  相似文献   

18.
In this article, we study a mixed problem with integral boundary conditions for a high-order partial differential equation of mixed type. We prove the existence and uniqueness of a strong solution. The proof is based on energy inequality and on the density of the range of the operator generated by the considered problem.  相似文献   

19.
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