具有θ型Calderón-Zygmund核的多线性奇异积分算子的端点估计

研究了一类具有θ型Calderon-Zygmund核的多线性奇异积分算子的有界性,得到它们是从L1(Rn)到弱L1(Rn)有界的．     

与非光滑核的奇异积分算子的Toeplitz算子的λ-中心BMO估计

设L是L~2(R~n)上的一个解析半群的无穷小生成元,核函数满足高斯上界.L~(-α/2)(0αn)是由L生成的广义分数次积分算子,若T_(j,1)是与L有关的带有非光滑核的奇异积分算子,或T_(j,1)=I,T_(j,2),T_(j,4)是线性算子且具有(B~(p,λ),B~(p,λ))有界性(1p∞,λ∈R),T_(j,3)=±I(j=1,2,…,m),其中I为恒等算子,M_b是乘法算子.当b∈CBMO~(p_2,λ_2)函数时,证明Toeplitz型算子θ_a~b是B~(p_1,λ_1)到B~(q,λ)上的有界算子,并由此得广义分数次积分交换子[b,L~(-a/2)]和非光滑核的奇异积分交换子[b,T]在中心Morrey型空间上的有界性.     

随机窗宽核估计L1模相合性

设X_1,…,X_n是来自某个具有分布F(x)和密度f(x)的d维总体的i.i.d.样本。为估计f(x),国内外统计学家提出了许多切合实际的估计,并在其相合性方面取得了大量的成果。随机窗宽核估计就是其中之一,见文献[1—3]等等。最近Breiman L.等,Devroye L.考虑了另一类型随机窗宽核估计即:     

CRW型交换子在Triebel-Lizorkin空间的有界性

本文考虑交换子[b,T]在 Triebel-Lizorkin 空间上的有界性,其中 b∈BMO(R~n),T 是卷积型奇异积分算子,其核为Ω∈L log~ L(S~(n-1)),给出了该交换子在 F_p~(s,p)(R~n)(s＞0,1＜p,q＜∞) 上有界的一个等价条件．     

一类粗糙奇异积分的加权 Triebel-Lizorkin有界性

本文研究了一类粗糙奇异积分算子的加权Triebel-Lizorkin有界性.对核函数Ω∈L log+L(Sn-1)建立了径向权函数的加权有界性;而对于核函数Ω∈Lr(Sn-1),1＜r≤∞,得到了一般的Muckenhopt权函数的加权有界性.     

CRW型交换子在Triebel-Lizorkin空间的有界性

本文考虑交换子[b,T]在Triebel-Lizorkin空间上的有界性,其中b∈BMO(Rn),T是卷积型奇异积分算子,其核为Ω∈Llog+L(Sn-1),给出了该交换子在Fs,qp(Rn)(s＞0,1＜p,q＜∞)上有界的一个等价条件.     

积域上一类奇异积分算子的L~p有界性

本文证明,对于Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)和P_(N_1),P_(N_2)∈(2),带粗糙核的奇异积分算子为L~p有界。     

一类粗糙奇异积分的加权Triebel-Lizorkin有界性

本文研究了一类粗糙奇异积分算子的加权Triebel-Lizorkin有界性.对核函数Ω∈Llog L(Sn-1)建立了径向权函数的加权有界性;而对于核函数Ω∈Lr(Sn-1),1相似文献   

抛物型积分算子的弱型极限行为

设0≤βα, q=α/(α-β), f≥0.本文研究带齐次核?的抛物型奇异积分和分数次积分算子的弱型极限行为,建立了如下结果:limλ→0+λqm({x∈Rn:Tα?,βf(x)λ})=1α||?||q q||f||q L1(Rn),以及limλ→0+λqm({x∈Rn:Tα?,βf(x)-?(x)ρ(x)α-β||f||L1(Rn)λ})=0,其中?满足Lqβ-Dini条件,当β=0时,还需满足∫Sn-1?(x′)J(x′)dσ(x′)=0.同时,给出了相应的抛物型极大奇异积分和Marcinkiewicz积分的弱型极限行为.此外,建立了关于Heisenberg群Hn上Hardy-Littlewood极大函数的相应结果.     

关于图的L(2,1)标号核图

图的L(2,1)标号核图来自频率分配问题而导致的图论问题.在本文中,我们证得(i)对任意简单图G,存在G的一个标号核图Gcore,使得L(G)=L(Gcore)和L(G)≥|V(Gcore)|-1;(ii)设图G有p个顶点且边集|E(G)|≠φ,存在路 Pi G(1≤i≤m)和路Hs G(1≤s≤n),其中在G中V(Pi)∩V(Pj)=φ(i≠j),在G中V(P,)∩V(Pt)=φ(s≠t),则有m∑t=1|V(Pt)|+n∑s=1|V(Hs)|-(m+n)≥p;(iii)G是p(p≥5)个顶点的简单图,则有p+3≤L(G)+L(G)≤3p-4.     

WEIGHTED BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL HARDY OPERATORS WITH BESOV-LIPSCHITZ FUNCTIONS

In this paper,we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions.The main result is that this kind of commutator,denoted by Hb α,is bounded from L x γp (R +) to Lx δ q (R +) with the bound explicitly worked out.     

齐型空间上L1与 BMO的内插空间

本文讨论齐型空间上L~1与BMO的内插空间,得到下列结果:对于0<θ<1,1≤q≤∞,有(L~1,BMO)_(θ,q)=L_(pq),其中θ=1-1/p.     

Hardy spaces H_L~p(R~n) associated with operators satisfying k-Davies-Gaffney estimates

Let L be a one-to-one operator of type ω having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k ∈ N. In this paper, the authors introduce the Hardy space HLp(Rn) with p ∈ (0, 1] associated with L in terms of square functions defined via {e-t2kL}t>0 and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schrdinger type operator L2 := (-Δ)k + Vk, where Δ is the Laplacian and 0≤V∈Llock(Rn). Moreover, as an application, for i ∈ {1, 2}, the authors prove that the associated Riesz transform ▽k(Li-1/2) is bounded from HLip (Rn) to Hp(Rn) for p ∈ (n/(n + k), 1] and establish the Riesz transform characterizations of HL1p (Rn) for p ∈ (rn/(n + kr), 1] if {e-tL1 }t>0 satisfies the Lr-L2 k-off-diagonal estimates with r ∈ (1, 2]. These results when k := 1 and L := L1 are known.     

弱Hardy空间上的参数型Marcinkiewicz积分(英文)

证明了参数型Marcinkiewicz积分μρΩ是(Hp,∞,Lp,∞)(0相似文献   

THE FUNDAMENTAL THEOREM OF INFORMATION TRANSMISSION FOR GENERAL MULTI-USER COMMUNICATION NETWORK SYSTEMS

In this paper, we first give a definition of the general multi-user communication network system, and introduce the coding type \[(\mathcal{U},\mathcal{Y},\mathcal{V})\] and \[({\mathcal{U}_0},\mathcal{Y},\mathcal{V})\], for the general network systems (cf Fig. 1, 2). We obtain the following results: 1. For the above \[(\mathcal{U},\mathcal{Y},\mathcal{V})\] type network system, in the general sequence model, the Shannon theorem of information transmission, the coding theorem of multi-user channel and their converse hold water; 2. The converse coding theorem holds water on the region \[D(\mathcal{L}_{L - J}^{({\text{n}})})\] (see(6.4)) for the general sequence model of \[({\mathcal{U}_0},\mathcal{Y},\mathcal{V})\]type network system; 3. On the memoryless multi-user channel for \[({\mathcal{U}_0},\mathcal{Y},\mathcal{V})\] type network system, the D(\[\mathcal{L}_{L - J}^{}\]) is an achievable vetes region For the memoryless multiple-access channel, the \[\mathcal{L}_{L - J}^{}\] is the capacity region, 4. For general \[({\mathcal{U}_0},\mathcal{Y},\mathcal{V})\] type multi-user communication network system, we set up a new decoding method, whick is said to be information threshold distinguishing decoding.     

Recurrence formulas for permanents of (0, 1)-circulants

A general method is developed for constructing linear recurrence formulas expressing the permanents of (0, 1)-circulants in terms of permanents of (0, 1)-circulants of the same type of lower orders. The method extends to all (0, 1)-circulants a result of N. Metropolis, M. L. Stein, and P. R. Stein on permanents of (0, 1)-circulants of a special type.     

Lambek calculus with one division and one primitive type permitting empty antecedents

The following assertion is proved: an inference rule given by a scheme is admissible in the Lambek calculus with one division L*(\) permitting empty antecedents if and only if it is admissible in the fragment of L*(\) with one primitive type L*(\; p ₁). To do that, a type substitution is used which reduces the derivability in L*(\) to the derivability in L*(\; p ₁).     

COMMUTATORS OF MULTIPLIERS ON HARDY SPACES

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.     

Lp-Norm inequality of the product of pseudo-differential operators involving Hankel transformation

Lp-norm type inequalities for pseudo-differential operators L(x,D) and H(x,D) are derived for 1 ≤ p < ∞. Product of pseudo-differential operators associated with Bessel operator Sμ are defined and its Lp-norm type inequalities are obtained.     

多线性向量值奇异积分极大算子的加权不等式

本文研究向量值奇异积分极大多线性交换子的性质,得到该算子的加权估计及加权弱型估计,作为该估计的推论可知算子T_(q,(?))~*在L~p(ω)上有界,其中ω∈A_p。当ω∈A_1时,满足加权L(logL)~(1/r)型估计。