One-dimensional average on spheres and approximation

In this paper, we consider the approximation of the degeneration of classic average on sphere on Hardy-Sobolev spaces I_λ(H^p) . We prove that the degenerate expression of average on sphere of an L^p function is convergent almost everywhere, and the speed of the approximation depends on λ. And when λ ≥ 2, the approximation of the average operator will be saturated. On the other hand, we also study the generalization of the average on the product of Hardy-Sobolev spaces.     

Oscillatory integrals on unit square along surfaces

Let Q ² = [0, 1]² be the unit square in two-dimensional Euclidean space ℝ². We study the L ^p boundedness of the oscillatory integral operator T _α,β defined on the set ℒ(ℝ²⁺ⁿ ) of Schwartz test functions by

Derivative estimates of averaging opera tors and extension

We study the derivative operator of the generalized spherical mean S^γt. By considering a more general multiplier m^Ωγ,b=Vn-2/2+γ(|ξ|)|ξ|^bΩ(ξ') and finding the smallest γ such that m^Ωγ,b is an Hp multiplier, we obtain the optimal range of exponents (γ,β,p)to ensure the H^p(R^n) boundedness of a^βS^γ1f(x). As an application, we obtain the derivative estimates for the solution for the Cauchy problem of the wave equation on H^p(R^n) spaces.     

Study of near-infrared nonvolatile two-center holographic recording in LiNbO3:Fe:Rh crystal

The near-infrared nonvolatile holographic recording has been realized in a doubly doped LiNbO₃:Fe:Rh crystal by the traditional two-center holographic recording scheme, for the first time. The recording performance of this crystal has been investigated by recording with 633 nm red light, 752 nm red light and 799 nm near-infrared light and sensitizing with 405 nm purple light. The experimental results show that, co-doped with Fe and Rh, the near-infrared absorption and the photovoltaic coefficient of shallow trap Fe are enhanced in this LiNbO₃:Fe:Rh crystal, compared with other doubly doped LiNbO₃ crystals such as LiNbO₃:Fe:Mn. It is also found that the sensitizing light intensity affects the near-infrared recording sensitivity in a different way than two-center holographic recording with shorter wavelength, and the origin of experimental results is analyzed.     

Herz-type Hardy spaces on Vilenkin groups and their applications

Let 1＜q＜∞, 1-1/q≤α＜∞, 0＜p＜∞ and G be a locally compact Vilenkin group.The authors first introduce the general Herz-type Hardy spaces HKα,pq(G) and hKα,pq(G), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces HKα,pq(G) of the fractional integral operators and the boundedness on the spaces hKα,pq(G) of the pseudo-differential operators of order zero.     

（Ce，Cu）：LiNbO3晶体非挥发全息记录理论研究与优化

根据双中心带输运模型，对（Ce，Cu）：LiNbO3晶体双中心非挥发全息记录进行了理论研究与优化。推导了（Ce，Cu）：LiNbO3晶体的微观参量，采用数值方法通过严格求解模拟双中心带输运方程来模拟全息记录过程。分析了记录过程中，记录与敏化光强、Ce和Cu掺杂浓度以及晶体微观参量对（Ce，Cu）：LiNbO3晶体双中心全息记录的影响。发现（Ce，Cu）：LiNbO3晶体非挥发全息记录中实现高衍射效率与固定效率的主导因素是深中心Cu，在记录过程中，深中心Cu建立起了很强的空间电荷场。数值模拟的结果经过实验验证，最高饱和与固定衍射效率别为60．5％和53．8％。     

Rough singular integral operators on Hardy-Sobolev spaces

The authors study the singular integral operator TΩ,αf(x)=p.v.∫R^nb(|y|Ω(y′)|y|^-n-αf(x-y)dy, defined on all test functions f, where b is a bounded function, α＞0, Ω(y′) is an integrable function on the unit sphere S^n-1 satisfying certain cancellation conditions. It is proved that, for n/(n α)＜p＜∞,TΩ,α is a bounded operator from the Hardy-Sobolev space H^pα to the Hardy space H^p. The results and its applications improve some theorems in a previous paper of the author and they are extensions of the main theorems in Wheeden‘s paper(1969). The proof is based on a new atomic decomposition of the space H^pα by Han, Paluszynski and Weiss(1995). By using the same proof,the singluar integral operators with variable kernels are also studied.     

Alokicenones A-H,eight tetrahydroanthracenes from the mangrove-derived Streptomyces sp. HN-A101

Alokicenones A-H (1–8), eight new tetrahydroanthracenes and one known okicenone (9) were identified from the secondary metabolites of mangrove-derived Streptomyces sp. HN-A101. Their structures were elucidated by HRESIMS and NMR spectroscopic data. The absolute configurations of them were determined by the calculated and experimental ECD curves. Compounds 1–2 and 9 showed moderate cytotoxicity against HCT116 and SW620 cancer cell lines with IC₅₀ values from 0.63 to 7.73?μM. In addition, compounds 1–3 and 7–9 also exhibited inhibitory activities against ROCK2 or BRD4.