球面Hardy空间上Riesz平均的逼近

引进了球面Hrady空间上Riesz平均算子及Peetre K模。讨论了Riesz平均算子在Hardy空间上的逼近性质。证明了Riesz平均算子与Peetre K模的强渐近等价关系。所得结果表明Peetre K模完全刻划了Riesz平均的逼近。     

正规实型黎曼对称空间上Riesz平均的几乎处处收敛性

设Ｘ＝Ｇ０／Ｋ０是非紧致黎曼对称空间，Ｇ０的李代数ｇ０是其复化李代数ｇ的正规实型．若记ｎ０＝ｄｉｍＸ，则我们在该文中证明：对于ｆ∈Ｌｐ（Ｘ），１≤Ｐ≤２，当复数ｚ满足Ｒｅｚ＞δ（ｎ０，Ｐ）＝（ｎ０－１）（１／Ｐ—１／２）时，ｆ关于拉普拉斯算子本征函数展开的ｚ阶Ｒｉｅｓｚ平均几乎处处收敛于ｆ．这一结论与经典的欧氏空间，以及复的和一秩的非紧致黎曼对称空间中完全相同．     

Hp(Ωn)(0＜p＜1)上临界阶Riesz平均强求和的逼近

本文讨论了球面上Hardy空间Hp(0＜p＜1)中Riesz平均的强求和在临界阶δ=n/p-n+1/2的有界性,并且建立了它和最佳逼近之间的关系.     

Besov空间B_1~(01)(R)上的Riesz平均

本文证明了任何正阶的 Riesz 平均在 Besov 空间(?)_1~(01)(R)上有界,而结论对0阶的 Riesz 平均不成立.因此,Riesz 平均关于空间(?)_1~(01)(R)的临界阶是0.     

紧对称空间上的最佳逼近和Fejer—Korovkin算子

引进了一秩紧对称空间上的Ｆｅｊｅｒ－Ｋｏｒｏｖｋｉｎ算子,通过建立Ｋ－泛函和光滑模的强渐近等价估计,研究了Ｆｅｊｅｒ－Ｋｏｒｏｖｋｉｎ算子的逼近性质,并由此给出了一秩紧对称空间上最佳逼近的基本定理。     

多维加权特殊原子空间上的Riesz平均算子

该文引入多维加权特殊原子空间并研究新型极大Ｒｉｅｓｚ平均算子在这些空间上的有界性。利用这种有界性，可以推出相应的Ｒｉｅｓｚ平均算子的几乎处处收敛性和多元算子插值等。     

紧对称空间上的最佳逼近和Fejér-Korovkin算子

引进了一秩紧对称空间上的Ｆｅｊéｒ－Ｋｏｒｏｖｋｉｎ 算子,通过建立Ｋ－泛函和光滑模的强渐近等价估计,研究了Ｆｅｊéｒ－Ｋｏｒｏｖｋｉｎ 算子的逼近性质,并由此给出了一秩紧对称空间上最佳逼近的基本定理．     

局部紧Abel群上的平移Riesz基和Riesz谱集

设G是局部紧Abel群,Ω■G是Haar可测集,L~2(Ω)是Ω上Haar平方可积函数构成的Hilbert空间,PW_Ω(G):={f∈L~2(G):supp f(ξ)■Ω}是G上的Paley-Wiener空间.本文研究Paley-Wiener空间PW_Ω(G)上平移Riesz基和Riesz谱集Ω之间的关系.     

子空间单位球的逼近紧性

设X是Banach空间,Y为X的子空间,B_X,B_Y分别是X和Y的闭单位球.本文研究B_Y的逼近紧性,证明了B_Y在X中是逼近紧的当且仅当对Y的每个与B_X相交的平移Y_T,Y_T∩B_X在Y_T中都是逼近紧的.还得到B_Y逼近紧的稳定性结果.     

紧Lie群上H~P（0＜P＜1）函数的临界阶Bochner－Riesz平均算子的有界性

本文利用尺度‖·‖＿（Ｈ（ｐ，∞））研究了一般紧Ｌｉｅ群上Ｈ￣ｐ函数的临界阶Ｂｏｃｈｎｅｒ－Ｒｉｅｓｚ平均算子的有界性，得到了如下结果：是（Ｈ￣ｐ，Ｈ（ｐ，∞））型的，并且其中Ｃ为与ｆ及Ｒ无关的常数。     

Riesz Means on Compact Riemannian Symmetric Spaces

We study approximation properties of the Riesz means on compact symmetric spaces of rank one. To do so we establish equivalences between the Riesz means and Peetre K-moduli and estimate the weak type and the uniform approximation of the Riesz means at the critical index. The relations between the Riesz means and the best approximation as well as the Cesàro means are also considered.     

Approximation Numbers of Identity Operators between Symmetric Sequence Spaces

We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Masty o, and Michels for identities l_pⁿF_n with an n-dimensional symmetric normed space F_n with p-concavity conditions on F_n and 1p2. We consider the general case of identities E_nF_n with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces E_n and F_n. We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Masty o, and Michels.     

紧致齐性空间上的调和分析（Ⅳ）─—Riesz变换与Bessel变换

本文研究了紧致齐性空间上的Ｒｉｅｓｚ位势算子与Ｂｅｓｓｅｌ位势算子，Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换，给出了上述算子对应的核函数的具体构造并证明了Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换作为奇异积分算子的Ｈ￣ｐ有界性，ｐ＞０。     

基本的局部实心Riesz空间

In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality.From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.     

Almost everywhere convergence of Riesz means on noncompact symmetric spaceSL(3,H)/Sp(3)

LetG/K be the noncompact Riemannian symmetric spaceSL(3,H)/Sp(3). We shall prove in this paper that forf∈L ^p(SL(3,H)/Sp(3)), 1≤p≤2, the Riesz means of orderz off with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge tof for Rez >δ(n,p). The critical index δ(n,p) is the same as in the classical Stein's result for Euclidean space, and as in the noncompact symmetric spaces of rank one and of complex type. Partially supported by National Natural Science Foundation of China     

Fourier-Laplace级数的强逼近

设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0 |Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1 ),其中Eλk(f)为Cesaro平均σλk的等收敛算子.     

Pointfree Spectra of Riesz Spaces

One of the best ways of studying ordered algebraic structures is through their spectra. The three well-known spectra usually considered are the Brumfiel, Keimel, and the maximal spectra. The pointfree versions of these spectra were studied by B. Banaschewski for f-rings. Here, we give the pointfree versions of the Keimel and the maximal spectra for Riesz spaces. Moreover, we briefly mention how one can use the results of this paper to give a pointfree version of the Kakutani duality for Riesz spaces.     

齐次群上的限制算子与Riesz平均

主要讨论一类齐次群上限制算子的映照性质,并且应用所得结果证明这类齐次群上Riesz平均的混合范数有界性。