共查询到20条相似文献,搜索用时 187 毫秒
1.
Yong DING Shan Zhen LU Qing Ying XUE 《数学学报(英文版)》2007,23(9):1537-1552
In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 (R^n) to L1 (R^n) and from the weak Hardy space H^1,∞ (R^n) to L^1,∞ (R^n), respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and (1, 1) and of type (p,p) for 1 〈 p 〈 2, respectively extension of some known results. 相似文献
2.
Zhang Pu Wu Huoxiong 《高校应用数学学报(英文版)》2005,20(4):455-461
Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO(R^n). It is proved that μΩ,bis bounded from the Hardy space H^1 (R^n) into the weak L^1(R^n) space. 相似文献
3.
Pu Zhang Jiukun Hua 《分析论及其应用》2005,21(3):226-234
Let T be the multiplier operator associated to a multiplier m, and [b, T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b,T] is bounded from the Hardy space H^1(R^n) into the weak L^1 (R^n) space and from certain atomic Hardy space Hb^1 (R^n) into the Lebesgue space L^1 (R^n), when the multiplier m satisfies the conditions of Hoermander type. 相似文献
4.
Bao Quan YUAN 《数学学报(英文版)》2008,24(2):253-266
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^*,γ(R^n), with 1〈p〈∞and A = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space. 相似文献
5.
Let Ф be a non-negative locally integrable function on R^n and satisfy some weak growth conditions, define the potential type operator TФ by TФf(x)=∫R^n Ф(x-y)f(y)dy. The aim of this paper is to give several strong type and weak type weighted norm inequalities for the potential type operator TФ. 相似文献
6.
The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p(R^n),P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p(R^n) into weak Lμ^p(R^n),1≤p〈∞. 相似文献
7.
In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ(f)(x)=(∫0^∞│∫│1-y│≤t Ω(x,x-y)/│x-y│^n-p f(y)dy│^2dt/t1+2p)^1/2 are investigated.It is proved that if Ω∈ L∞(R^n) × L^r(S^n-1)(r〉(n-n1p'/n) is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p(R^n) to L^p(R^n) for 1 〈 p ≤ max{(n+1)/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type(p,p) for 1 〈 p ≤ 2,of the weak type(1,1) and bounded from H1 to L1. 相似文献
8.
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
9.
Pu Zhang 《数学学报(英文版)》2010,26(9):1709-1722
Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO(R^n). The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially. 相似文献
10.
For the potential type operator
TФf(x)=∫RnФ(x-y)f(y)dy,
where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type (p,q) inequality for TФ is obtained. 相似文献
TФf(x)=∫RnФ(x-y)f(y)dy,
where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type (p,q) inequality for TФ is obtained. 相似文献
11.
In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = (α+β)/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p(R^n) is obtained. 相似文献
12.
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
13.
Shan Zhen LU Li Fang XU 《数学学报(英文版)》2006,22(1):105-114
In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ(R^n)(0 〈β≤ 1/m) and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on the Hardy type spaces Hb^m^p,n(R^n) and the Herz Hardy type spaces Hbm Kq^α,p(R^b). 相似文献
14.
Mirjana STOJANOVIC 《数学物理学报(B辑英文版)》2013,33(6):1721-1735
We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C^∞(t∈(0,∞);H2^s+2(R^n))∩C^0(t∈[0,∞);H^s(R^n)),s∈R,to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions ∫0^2p(β)D*^βu(x,t)dβ=△xu(x,t)+f(t,u(t,x)),t≥0,x∈R^n,u(0,x)=φ(x),ut(0,x)=ψ(x),(0.1) where △xis the spatial Laplace operator,D*^β is the operator of fractional differentiation in the Caputo sense and the force term F satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval (0, 2), i.e., p(β) =m∑k=1bkδ(β-βk),0〈βk〈2,bk〉0,k=1,2,…,m.The regularity of the solution is established in the framework of the space C^∞(t∈(0,∞);C^∞(R^n))∩C^0(t∈[0,∞);C^∞(R^n))when the initial data belong to the Sobolev space H2^8(R^n),s∈R. 相似文献
15.
Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group and also a smooth hypersurface in B(R^n) with the dimension n × n. 相似文献
16.
Jiang Liya Chen Jiecheng 《高校应用数学学报(英文版)》2006,21(1):69-78
The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i|x|^aΩ(x)|x|^-n is studied,where a∈R,a≠0,1 and Ω∈L^1(S^n-1) is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω(x' )∈Llog+L(S^n-1 ), the Fp^a,q(R^n) boundedness of the above operator is obtained. Meanwhile ,when Ω(x) satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 (R^n). 相似文献
17.
Yan Ping Chen 《数学学报(英文版)》2009,25(6):983-1000
In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2(R^n) to the Lebesgue space L^2(R^n), which is a substantial improvement and extension of some known results. 相似文献
18.
The (L^p, Fp^β,∞)-Boundedness of Commutators of Multipliers 总被引:1,自引:0,他引:1
Pu ZHANG Jie Cheng CHEN 《数学学报(英文版)》2005,21(4):765-772
In this paper, we study the commutator generalized by a multiplier and a Lipschitz function. Under some assumptions, we establish the boundedness properties of it from L^P(R^n) into Fp^β,∞(R^n), the Triebel Lizorkin spaces. 相似文献
19.
In this note, we give a new proof of subcritical Trudinger-Moser inequality on R^n. All the existing proofs on this inequality are based on the rearrangement ar-gument with respect to functions in the Sobolev space W^1,n (R^n). Our method avoids this technique and thus can be used in the Riemamlian manifold case and in the entire Heisenberg group. 相似文献
20.
G. Dziuk C.M. Elliott 《计算数学(英文版)》2007,25(4):385-407
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n+1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. 相似文献