共查询到20条相似文献,搜索用时 109 毫秒
1.
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
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.
应用核的分解,讨论了粗糙核奇异积分算子
Tf(x)=p.v.∫R^nΩ(x-y)/|x-y|^nf(y)dy
和BMO(R^n)函数b生成的交换子[b,T]的有界性.证明了当Ω∈L(logL)^2(S^n-1)时,[b,T]是Triebel—Lizorhn空间Fp^α,q(R^n)上的有界算子. 相似文献
4.
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
5.
Hans TRIEBEL 《数学学报(英文版)》2008,24(4):539-554
A space Apq^s (R^n) with A : B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp(Г), where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D(R^n/Г) is dense in it. Related dichotomy numbers are introduced and calculated. 相似文献
6.
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
7.
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
8.
Jia-cheng Lan 《应用数学学报(英文版)》2005,21(4):615-622
In this paper, the author discusses the multilinear singular integrals with certain θ-type Calderdn- Zygmund operators and obtain the boundedness from weak H^1 (R^n) to weak L^1 (R^n). 相似文献
9.
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
10.
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
11.
Marcinkiewicz积分交换子在Herz型空间中的弱型估计 总被引:1,自引:0,他引:1
用μΩ表示Marcinkiewicz积分,μΩ,b表示μΩ与函数b∈BMO(R~n)生成的交换子.本文证明了交换子μΩ,b是从Herz型Hardy空间H■_q~(n(1-(1/q)),p)(R~n)到弱Herz空间W■_q~(n(1-(1/q)),p)(R~n)有界的,其中0<p≤1,1<q<∞. 相似文献
12.
Zun-wei FU~ 《中国科学A辑(英文版)》2007,50(10):1418-1426
In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 < p1 <∞, 0 ≤β< n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained. 相似文献
13.
本文讨论了Rn 上如下一类带临界增长的拟线性椭圆方程正解的存在性 :-div(| u|p- 2 u) -axn| u|p- 2 u xn +|u|p- 2u=up - 1 ,xn ≠ 0 ,x∈Rn.这里 ,1
相似文献
14.
Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the LP(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed 1 < p <∞ are obtained. 相似文献
15.
The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (-Δ) -α/2 are extended to the generalised fractional integrals L-α/2 for 0 < α < n, where L =-div A is a uniformly complex elliptic operator with bounded measurable coefficients in Rn. 相似文献
16.
§1. IntroductionLet L be a homogeneous elliptic operator on L2(Rn) of order 2m in divergence formL = (?1)m|α|=|β|=m?α(aα,β?β), (1.1)where we assume aα,β ∈ L∞(Rn;C) for all α,β. The operator L is associated to the followingform Q(f,g) de?ned o 相似文献
17.
Xiaoping Pan Xiyan Hu Lei Zhang College of Mathematics Econometrics Hunan University Changsha China. 《高等学校计算数学学报(英文版)》2006,15(3):227-236
Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived. 相似文献
18.
本文研究快速扩散方程ut-Δum +| u|p =0的柯西问题 ,其中m ,p∈ ( 0 ,1) .对于 0
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19.
高红亚 《中国科学A辑(英文版)》2003,46(4)
In this paper, we first give the definition of weakly (K1, K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any ql that satisfies 0 < K1n(n+4)/22n+1 × 100n2[23n/2(25n + 1)](n - q1) < 1, there exists p1 = p1(n, q1, K1, K2) > n, such that any (K1, K2)-quasiregular mapping f ∈W(loc)(1,q1)(Ω,Rn) is in fact in W(loc)(1,p1)(Ω,Rn). That is, f is (K1, K2)-quasiregular in the usual sense. 相似文献
20.
Yuxian Zheng 《分析论及其应用》2006,22(2):136-140
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1. 相似文献