多线性Calderón-Zygmund算子的加权有界性

建立了多线性Calderón-Zygmund算子在比幂权空间更一般的Herz空间和Herz型Hardy空间上的有界性.作为推论,得到了该算子的幂权估计.在这些幂权估计中,权指标可以突破Ap权的指标限制,显示出和经典Calderón-Zygmund算子本质的区别.     

各向异性函数空间上的多线性算子的估计及其应用

设A是Rn上的各向异性伸缩,L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lp(Rn)到无权的各向异性Hardy空间HpA(Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOwA(Rn)得到包含关系:BMOX(Rn)(...     

MULTILINEAR CALDER(O)N-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderón-Zygmund operator can be obtained.     

(log,θ)-Calderon-Zygmund算子在H~p中的有界性(英文)

本文我们在条件∫１０θｐ（ｔ）／ｔ１＋ｎ（１－ｐ）ｄｔ＜＋∞下，讨论了（ｌｏｇ，θ）－Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子在Ｈｐ（Ｒｎ），（０＜ｐ≤１）中的有界性．     

Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.     

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

Spaces of type BLO on non-homogeneous metric measure

Let (, d, μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this paper, we introduce the space RBLO(μ) and prove that it is a subset of the known space RBMO(μ) in this context. Moreover, we establish several useful characterizations for the space RBLO(μ). As an application, we obtain the boundedness of the maximal Calderón-Zygmund operators from L ^∞(μ) to RBLO(μ).     

多线性算子在Herz型Hardy空间上的有界性

本文证明了Ｒｎ上奇异积分乘积之有限和的多线性算子是从ＨＫｑ１α１,ｐ１（Ｒｎ）×… ×ＨＫｑｋαｋ,ｐｋ（Ｒｎ）到ＨＫｑα,ｐ（Ｒｎ）有界的,如果它满足由目标空间所确定的直到一定阶的消失矩条件．这些多线性算子所满足的消失矩条件,当αｊ≥０时也是必要的．而且,这里所考虑的奇异积分包括Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ奇异积分及任意阶的分数次积分．     

Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|＜(?) andmax{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p≤∞ and 0＜q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p＜∞ and max{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s＝0 and q＝2,thenH(?)_∞q~s(X)＝(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)＝BMO(X).     

关于Calderón-Zygmund 算子在加权Morrey 空间上的一些交换子估计

设T 是一个Calderón-Zygmund 奇异积分算子. 本文将采用统一的Sharp 极大函数估计的方法来证明当权函数w 满足一定条件时, 交换子[b, T] 在加权Morrey 空间L^p,k(w) 上的有界性质, 其中符号b 属于加权BMO 空间、Lipschitz 空间和加权Lipschitz 空间.