关于复平面上H~∞空间,β~p空间以及β_0~p空间的几个问题

本文讨论了单位圆中Hardy空间H∞到p-Bloch空间βP的复合算子T1.φ加权复合算子Tψ,(?)的有界性,也讨论了H∞到小p-Bloch空间β6的复合算子T1,(?)的有界性问题;另外还讨论了小p-Bloch空间到H∞空间的点乘子及小p-Bloch空间上复合算子的紧性等.     

Cn中单位球上几个全纯函数空间上加权复合算子的有界性

讨论了C^n上单位球中p-Bloch空间上加权复合算子Tφ，ψ的有界性，得到Tφ，ψ是β′到β′有界算子的几个充分条件，此外还讨论了p-Bloch空间和小p-Bloch空间上复合算子T1，ψ的有界性，得到了几个充分条件和必要条件，就单位球的情形扩展了[2]的结论．     

两个解析函数空间之间的加权复合算子

本文刻画了空间F(p,q,s)到空间β~α之间加权复合算子T_((?),ψ),的有界性和紧性条件并得到了一系列相关结果．     

小Bloch型空间上的加权复合算子

本文将刻划从小Bloch型空间β0p到β0q(0＜p,q＜∞)上加权复合算子Tψ,ψ的有界性和紧性.同时得到了Tψ,ψ是Bloch型空间βp到βq(p＞1,0≤q≤1)有界算子的充要条件以及Tψ,ψ是Bloch型空间βp到βq(0≤p,q＜∞)紧算子的充要条件.     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,ψ的有界性和紧性以及加权复合算子Tψ,ψ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,ψ的有界性问题.主要得到以下结论(i)Tψ,ψ是空间βp到βq的有界算子之充要条件;(ii)T1,ψ是空间βp到βq的紧算子之充要条件;(iii)T1,ψ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,δ的有界性和紧性以及加权复合算子Tφ,δ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,φ的有界性问题.主要得到以下结论: (i)Tφ,δ是空间βp到βq的有界算子之充要条件; (ii)T1,φ是空间βp到βq的紧算子之充要条件; (iii)T1,φ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

单位球上F(p,q,s)空间到Bloch型空间的复合算子

该文分别给出了单位球B上空间F(p, q, s)到空间β^α之复合算子C_{varphi}为有界算子和紧算子的充要条件.同时作为推论获得了Bloch型空间的相应结果.     

Cn中空间F(p,q,s)到βq+n+1/p的复合算子

对一切P＞0,s≥0和q＞q＞max{-n-1,-s-1},给出了单位球上一般函数空间F(p,q,s)到Bloch型空间βq+n+1/p之复合算子Cψ有界和紧的充要条件,并给出了几个推论.     

Hardy空间到加权Hardy空间上的复合算子

本文研究了从Hardy空间到加权Hardy空间上的复合算子,并给出此复合算子为有界和紧的条件。     

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

Some Remarks on Complex Crowns of Riemannian Symmetric Spaces

We discuss several results and problems in which complex geometric constructions appear in the geometry of real pseudo Riemannian symmetric spaces in connection with analysis on such spaces.     

Analytic Hilbert Spaces over the Complex Plane

In this paper, we study the structure of quasi-invariant subspaces of analytic Hilbert spaces over the complex plane. We especially investigate when two quasi-invariant subspaces are similar or unitarily equivalent for an analytic Hilbert space over the complex plane.     

Shift Generated Haar Spaces on Compact Domains in the Complex Plane

Haar spaces are certain finite-dimensional subspaces of $\cc(K)$, where $K$ is a compact set and $\cc(K)$ is the Banach space of continuous functions defined on $K$ having values in $\C$. We characterize those Haar spaces which are generated by shifts applied to a single, analytic function for $K\subset\C$. This means that an arbitrary finite number of shifts generates Haar spaces by forming linear hulls. We have to distinguish two cases: (a) $K\not=\overline{K^\circ}$; (b) $K=\overline{K^\circ}$. It turns out that, in case (a), an analytic Haar space generator for dimensions one and two is already a universal Haar space generator for all dimensions. The geometrically simplest case that, in case (b), $K$ is convex with smooth boundary turns out to be the most difficult case. There is one numerical example in which the entire function $f:=1/\Gamma$ is interpolated in a shift generated Haar space of dimension four.     

Remarks on Herz-Type Hardy Spaces

Basic properties of the Herz-type Hardy spaces , such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0 < q < ∞. Partly supported by the Grants-in-Aid for Scientific Research (A)(1)11304009, (B)(1)10440046, Japan Society for the Promotion of Science.     

Some Remarks on Orlicz-Lorentz Spaces

Spaces of Lorentz type called Orlicz-Lorentz spaces are studied. There are given necessary and sufficient conditions for the spaces to be order continuous, separable, KB-spaces and to contain isometric or isomorphic copy of l∞ or c₀. Moreover a criterion for strict convexity of these spaces is found.     

极空间的注记

本文中我们提到的极空间的秩不必是有限的。得到的主要结果是，令S是一个不可约的极空间，如果p～q，p～q是S中的点，则有极空间是同构的，我们把它记作     

Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane

We study the boundedness of the Cauchy singular integral operators on curves in complex plane in generalized Morrey spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of singular integral operators in weighted generalized Morrey spaces.     

Some Modular Inequalities in Lebesgue Spaces with Variable Exponent on the Complex Plane

Mathematical Notes - We consider the modular inequalities for some linear operators on Lebesgue spaces with variable exponent on the complex plane. The main results show that the variable exponent...