共查询到18条相似文献,搜索用时 0 毫秒
1.
GuoEnHU 《数学学报(英文版)》2003,19(2):397-404
The L^2(R^n) boundedness for the multilinear singular integral operators defined by TAf(x)=∫R^nΩ(x-y)/|x-y|^n 1(A(x)-A(y)-△↓A(y)(x-y))f(y)dy is considered,where Ω is homogeneous of degree zero,integrable on the unit sphere and has vanishing moment of order one,A has derivatives of order one in BMO(R^n) boundedness for the multilinear operator TA is given. 相似文献
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GuoEnHU BoLinMA 《数学学报(英文版)》2004,20(5):785-792
The commutators of singular integral operators with homogeneous kernel Ω(x)/|x|^n are studied, where Ω is homogeneous of degree zero, and has mean value zero on the unit sphere. It is proved that Ω∈ L(logL)^(k 1)(S^(n-1)) is a sufficient condition such that the k-th order commutator is bounded on L^2(R^n). 相似文献
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DunYanYAN GuoEnHU 《数学学报(英文版)》2005,21(1):209-214
In this paper, the authors discuss a class of multilinear singular integrals and obtain that the operators are bounded from H^1(R^n) to weak L^1(R^n). Using this result, we can directly prove a main theorem in [5]. 相似文献
4.
Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
5.
Yong Zhong SUN Wei Yi SU 《数学学报(英文版)》2005,21(6):1249-1258
It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P(R^n), 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO. 相似文献
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§1. IntroductionAlocallyintegrablefunctionf(x)belongstoLipα(Rn),ifthereisaconstantC,suchthatforeveryx,y∈Rn|f(x)-f(y)|≤C|x-y|α ThesmallestconstantCsatisfiesaboveiscalledLipschitznormoffandisdenotedbyyfy∧α.By[1],f∈Lipα(Rn)equivalenttof∈εα,2,whereεα,2=… 相似文献
7.
ShanZhenLU GuiPingTAO 《数学学报(英文版)》2003,19(4):645-654
In this paper,the authors establish the weighted (L^p,L^q) estimates for a class of multilinear oscillatory singular integrals with smooth phases.Certain endpoint estimates are also considered. 相似文献
8.
Littlewood-Paley operator,the function g(f),is considered as an operator on BMO(T).It is proved that if f∈BMO(T),then g(f)∈BMO(T) and there is a constant C that is independent of f such that ||g(f)||*≤C||f||*.Moreover,we have got the further results. 相似文献
9.
Let L =-△ + V be the Schr dinger operator on Rd, where △ is the Laplacian on Rdand V≠0 is a nonnegative function satisfying the reverse H lder's inequality.The authors prove that Riesz potential Iβand its commutator [b, Iβ] associated with L map from Mp,qα,vinto Mp1,q1α,v. 相似文献
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Potential Analysis - We obtain boundedness results for the higher order commutators of singular integral operators between weighted Lebesgue spaces, including Lp-BMO and Lp-Lipschitz estimates. The... 相似文献
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Let L=??+V be the Schr ¨odinger operator on Rd, where?is the Laplacian on Rd and V 6=0 is a nonnegative function satisfying the reverse H¨older’s inequality. The authors prove that Riesz potential Iβa... 相似文献
14.
Bin Lin DAI Ai Nong FANG 《数学学报(英文版)》2005,21(3):465-472
In this paper, we will study the nonelementary groups of MSbius transformations in R^n and some properties are obtained. Also in this paper we will prove several theorems about discreteness criteria and group convergence of nonelementary groups of M(R^n). 相似文献
15.
Solvability of the Dirichlet Problem in W~(2,p )for a Class of Elliptic Equations with Singular Data
Loredana CASO 《数学学报(英文版)》2014,30(5):737-746
We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces. 相似文献
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Yin Sheng JIANG Ming Ju LIU Lin TANG 《数学学报(英文版)》2005,21(3):577-584
Some estimates for the convolution operators with kernels of type (l, r) on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established. 相似文献