共查询到20条相似文献,搜索用时 31 毫秒
1.
王传荣 《数学物理学报(B辑英文版)》2005,25(2):376-384
This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it‘s a linear bounded operator of space H^α(L)(rn, s). Then Plemelj formula and some other properties for random singular integral are proved. 相似文献
2.
极大奇异积分算子的一个BLO估计 总被引:1,自引:0,他引:1
本文研究以(Ω(x)/|z|n))为核的极大齐次奇异积分算子在空间BMO(R~n)上的性质,其中Ω是一个零阶齐次函数且在单位球面上均值为零.可以证明:若Ω满足某种最小尺度条件和某种L~1-Dini型正则性条件,则此极大奇异积分算子是由BMO(R~n)到BLO(R~n)的有界算子. 相似文献
3.
In this paper, a kind of new definitions of singular integral operators in the weighted L2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L2 space with Jacobi weights are given. 相似文献
4.
本文研究了带粗糙核的奇异积分算子与BMO函数生成的交换子的有界性问题.利用原子分解的方法,获得了带粗糙核的奇异积分交换子TΩb在Lp空间、Hardy空间、弱Hardy空间上的有界性结果,推广了交换子Tb在各类函数空间上有界性的结果. 相似文献
5.
《数学学报(英文版)》2016,(8)
In this paper,we study the L~p mapping properties of certain class of maximal oscillatory singular integral operators.We prove a general theorem for a class of maximal functions along surfaces.As a consequence of such theorem,we establish the L~p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L(S~(n-1)).Moreover,we highlight some additional results concerning operators with kernels in certain block spaces.The results in this paper substantially improve previously known results. 相似文献
6.
7.
Stephen T. Welstead 《Integral Equations and Operator Theory》1985,8(3):402-426
Cauchy singular integral operators are characterized as operators in a weighted L2-space. The integral operator arises from a singular integral equation with variable coefficients. An appropriate weight function associated with the singular integral operator is constructed, and the set of polynomials orthogonal with respect to this weight function is defined. The action of the operator on polynomial sets is studied, and the definition of the operator is extended to a weighted L2-space. In this space, the operator is shown to be bounded, and, in some cases, isometric. Formulas are developed for the composition of the singular integral operator and its one sided inverse. 相似文献
8.
积域上的一类粗糙奇异积分算子 总被引:4,自引:0,他引:4
本文讨论了积域Rn×Rm上一类带粗糙核的奇异积分算子Tf(x,y)=p.v.Rn×RmΩ(u,v)|u|n|v|mh(|u|,|v|)f(x-u,y-v)dudv的Lp(Rn×Rm)有界性.这里,Ω为原子Hardy空间H1a(Sn-1×Sm-1)中的函数且h为空间l∞(Lq)(R+×R+)中的径向函数. 相似文献
9.
<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates of rough maximal functions along surfaces with applications 下载免费PDF全文
In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn-1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results. 相似文献
10.
This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem. 相似文献
11.
Non-linear singular integral equations are investigated in connection with some basic applications in two-dimensional fluid mechanics. A general existence and uniqueness analysis is proposed for non-linear singular integral equations defined on a Banach space. Therefore, the non-linear equations are defined over a finite set of contours and the existence of solutions is investigated for two different kinds of equations, the first and the second kind. Moreover, the existence of solutions is further studied for non-linear singular integral equations over a finite number of arbitrarily ordered arcs. An application to fluid mechanics theory is finally given for the determination of the form of the profiles of a turbomachine in two-dimensional flow of an incompressible fluid. 相似文献
12.
Yi Huang 《Archiv der Mathematik》2018,111(6):633-646
In this article we generalize the singular integral operator theory on weighted tent spaces to spaces of homogeneous type. This generalization of operator theory is in the spirit of C. Fefferman and Stein since we use some auxiliary functionals on tent spaces which play roles similar to the Fefferman–Stein sharp and box maximal functions in the Lebesgue space setting. Our contribution in this operator theory is twofold: for singular integral operators (including maximal regularity operators) on tent spaces pointwise Carleson type estimates are proved and this recovers known results; on the underlying space no extra geometrical conditions are needed and this could be useful for future applications to parabolic problems in rough settings. 相似文献
13.
In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given. 相似文献
14.
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions. 相似文献
15.
Calderon-Zygmund奇异积分算子交换子在Herz型Hardy空间中的有界性 总被引:2,自引:0,他引:2
本文证明了交换子[6,T]在一类Herz型Hardy空间中的强型与弱型有界性估计,其中6∈BMO(Rn),T为Calderon-zygmund奇异积分算子。 相似文献
16.
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 Hlder 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 Hlder continuous property on the boundary. 相似文献
17.
L2 estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of almost orthogonality, oscillatory estimates and size estimates. 相似文献
18.
设T 是一个Calderón-Zygmund 奇异积分算子. 本文将采用统一的Sharp 极大函数估计的方法来证明当权函数w 满足一定条件时, 交换子[b, T] 在加权Morrey 空间Lp,k(w) 上的有界性质, 其中符号b 属于加权BMO 空间、Lipschitz 空间和加权Lipschitz 空间. 相似文献
19.
Summary In a previous paper the authors proposed a modified Gaussian rule
*
m
(wf;t)to compute the integral (wf;t) in the Cauchy principal value sense associated with the weightw, and they proved the convergence in closed sets contained in the integration interval. The main purpose of the present work is to prove uniform convergence of the sequence {
*
m
(wf;t)} on the whole integration interval and to give estimates for the remainder term. The same results are shown for particular subsequences of the Gaussian rules
m
(wf;t) for the evaluation of Cauchy principal value integrals. A result on the uniform convergence of the product rules is also discussed and an application to the numerical solution of singular integral equations is made. 相似文献
20.
In this article,the authors discuss a kind of modified singular integral equations on a disjoint union of closed contours or a disjoint union of open arcs.The authors introduce some singular integral operators associated with this kind of singular integral equations,and obtain some useful properties for them.An operatorial approach is also given together with some illustrated examples. 相似文献