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.     

ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.     

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).     

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   

乘积空间上粗糙Marcinkiewicz积分算子的一点注记

本文将证明对于Ω∈L(log+L)2(Sn-1×Sm-1),∫sn-1Ω(x′,y′)dx′=0(Ay′∈Sm-1),∫sm-1 Ω(x′,y′)dx′=0(Ax′∈Sn-1)以及h∈L∞(R1+,R1+),积域上Marcinkiewicz积分算子μΩ,h为Lp(Rn×Rm)有界,其中1＜p＜∞.从而改进了以往结果.     

带变量核的Marcinkiewicz积分交换子的加权Lipschitz估计

利用Sharp极大函数,证明了带变量核的Marcinkiewicz积分算子μΩ和某一类加权Lipschitz空间的函数b生成的交换子μbΩ是由Lp(v)到Lq(v1-q)的有界算子.     

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h be a measurable function defined on R+×R+. LetΩ∈ L(log L+)νq(Sn1-1×Sn2-1)(1 ≤νq≤ 2) be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral T f(x1, x2) = p. v.∫ Rn1+n2Ω(y′1, y′2)h(|y1|, |y2|)|y1|n1|y2|n2f(x1- y1, x2- y2)dy1dy2maps from Sα1, α2p, q˙F(Rn1× Rn2) boundedly to itself for 1 p, q ∞, α1, α2 ∈ R.     

关于广导算子的零空间

本文讨论了两类广义导算子δＡＢ（ｘ）＝Ａｘ－ｘＢ和τＡＢ（ｘ）ＡｘＢ－Ｘ，并给出了一些成立的充分必要条件     

SHARP MAXIMAL FUNCTION ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS WITH NON-SMOOTH KERNELS

In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.     

具有齐性核的Marcinkiewicz积分在Herz型Hardy空间的有界性

本文讨论了具有齐性核的Marcinkiewicz积分μΩ在Herz型Hardy空间的有界性,证明了μΩ是从HKqα,p(Rn)到Kqα,p(Rn)有界的.     

具有齐性核的Marcinkiewicz积分在Herz型Hardy空间的有界性

本文讨论了具有齐性核的Marcinkiewicz积分μΩ在Herz型Hardy空间的有界性,证明了μΩ是从HKqa,p(Rn)到Kqa,p(Rn)有界的.     

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.     

一类带有变量核的积分算子在Herz型Hardy空间的有界性

本文研究了带有变量核的奇异积分与分数次积分算子.当核函数满足一类Dini型条件时,证明了 这类算子从Herz型Hardy空间到Herz空间的有界性.     

一类带有变量核的积分算子在Herz型Hardy空间的有界性

本文研究了带有变量核的奇异积分与分数次积分算子.当核函数满足一类Dini型条件时,证明了这类算子从Herz型Hardy空间到Herz空间的有界性.     

ON THE PROBLEMS OF THE INFINITESIMAL DEFORMATION OF THE SURFACES OF REVOLUTION WITH MIXED CURVATURE

In this paper the problem of the infinitesimal deformation of the surfaces of revolution with mixed Ganss curvature is studied. In connection with this problem a differential equation of mixed type, which belongs to the second degenerate type, in the form , \[k(\rho ){w_{\rho \rho }} + {w_{\theta \theta }} + \rho {w_\rho } = 0({\rho _1} < \rho < {\rho _2},0 \leqslant \theta \leqslant 2\pi )\] is obtained, where w is the component of the displacement vector of the infinitesimal deformation in the direction of the rotation axis, and\[k(\rho ) = \rho {z^'}(\rho )/{z^{'}}(\rho ),z(\rho )\] being the meridian curve of the surface of revolution. Suppose a surface of revolution S has two holes \[{L_1}(\rho = {\rho _1})\] and \[{L_2}(\rho = {\rho _2})\], then the meridian of the surface satisfies the condition \[{z^'}(\rho ) = 0\] on \[\rho = {\rho _0}({\rho _1} < {\rho _0} < {\rho _2})\]. If the Gauss curvature K of the surface is a strictly monotone increasing function of \[\rho \], \[{K^'}(\rho ) > 0,{\rho _1} < \rho < {\rho _2}\],then the surface S does not permit of the non-trivial sliding on the plane containing the boundary L2 of the surface. The rigidity of the surface is proved by the energy integral method. Moreover, the uniqueness of the Tricomi problem, the generalized Tricomi problem, the degenerate Tricomi problem and the Frankl's problem for a piece of surface with mixed curvature are studied.     

BOUNDEDNESS OF GENERALIZED MARCINKIEWICZ INTEGRAL ON THE H~p-SOBOLEV SPACES

§ 1　IntroductionIn this paper,we consider the following general Marcinkiewicz integral:μΩ,αf (x) =∫∞0 ∫|x- y|≤ tΩ (x -y)| x -y| n- 1 f(y) dy2 dtt3+2α1 2 (1 .1 )for all f∈ S(Rn) ,α≥ 0 ,andΩ is a distribution kernel.Whenα=0 ,it is the classicalMacinkiewicz integral operator many mathematicians have studied.There are a lot ofreferences about the topic that you can find.Here we take a simple list of some results ofthis topic.In 1 958,Stein[8] firstproved that ifΩ∈ Lipα(Sn- 1…     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi-Reinhardt的概念并求出了其完备标准正交函数系.     

THE APPROXIMATE COMPUTATION OF HYPERSINGULAR INTEGRALS ON INTERVAL

In this paper some numerical methods for computing hypersingular integrals on interval are given. Using geometric meshes, these methods lead 10 an exponential convergence in the range of engineering compulation. A numerical example shows their effeclivity and accuracy.