齐次群上多线性奇异积分算子的有界性

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

Decomposition of the Space of Regular Operators

Let E be a directed vector space with the Riesz decomposition property and F be a complete v?ctor lattice. It is proved that if G is a solid subspace of E then the subspace of all regular operators annihilating on G is a component in the space of all regular operators from E into F.¹²     

Boundedness of fractional integral operators in Herz-type spaces on locally compact Vilenkin groups

Let G be a locally compact Vilenkin group. In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaceson G are obtained.     

BOUNDEDNESS OF FRACTIONAL INTEGRAL OPERATORS IN HERZ—TYPE SPACES ON LOCALLY COMPACT VILENKIN GROUPS

Let G be a locally compact Vilenkin group.In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G.Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obtained.     

有界局部紧Vilenkin群上的广义Calderón-Zygmund算子(英文)

记Ｇ为一有界局部紧的Ｖｉｌｅｎｋｉｎ群．我们引进了Ｇ上的一类Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ型算子,并且证明了它们的加权ＬＰ（Ｇ）有界性．另外还给出了这些结果的一些应用．     

包含紧算子理想的Toeplitz算子代数的刻画

设G为一个torsion-free的离散群,（G,G＋）为一个拟序群,记T^G (G)为相应的Toeplitz算子代数,K(l^2(G 1)为l^2(G )上的紧算子全体,本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。（1）（G,G＋）为一个序群,（2）G中存在一个最小的正元。     

某些算子在局部紧的Vilenkin群上的Herz型Hardy空间

G表示局部紧的Vilenkin群， 在论文中作者将研究某些次线性算子和Calderón Zygmund算子在Herz型Hardy空间上的有界性.      

On the sharpness of non-optimal approximation for semigroup operators

The sharpness of the rate of approximation by certain operators to the identity is considered in the sense that there exist smooth elements such that a rate (given by a direct theorem) cannot be improved. The operators dealt with are semigroup operators, the Cesàro means of these, as well as the associated resolvent operators.Dedicated to Professor H. G. Tillmann on the occasion of his 60th birthday on Sept. 30, 1984, in friendship and admiration     

Some Remarks on Singular Integrals and Power Weights on Vilenkin Groups

Let G be a Vilenkin group and T a sublinear operator. The author investigates under what weak conditions on the size of T, the Lp(G)-boundedness of T implies its Lp|x|α (G)-boundedness. For those sublinear operators which map Lp(G) to Lq(G) with p < q the author also obtains some similar results.     

Best approximation by polynomial operators in banach spaces

The problem of approximation in the space of bounded linear operators ? (E;G) between normed spaces E and G by compact operators has been extensively studied in the last few years.

Recently Deutsch, Mach and Saatkamp ([2]) have considered the problem of approximating elements of ?(E;G) by the subset K _N(E;G) of operators whose range is at most N dimensional. We consider in this paper the problem of approximating operators (not necessarily linear) beteen normed spaces E and G by continuous homogeneous polynomials, and in particular by such polynomials which have finite-dimensional range.     

局部紧Vilenkin群上弱Morrey-Herz空间中一些算子的有界性

首先引入了一个新空间—局部紧Vilenkin群G上弱齐次Morrey-Herz空间WMK_(p,q)~(α,λ)(G),然后在WMK_(p,q)~(α,λ)(G)上讨论了一些奇异积分算子和分数次奇异积分算子的有界性问题.     

Local semigroups of contractions and some applications to Fourier representation theorems

It is proved that every local semigroup of contraction operators can be dilated to a group of unitary operators. Applications to some problems related with results of M. G. Krein, Bochner and Koosis are given.     

Vilenkin群上Morrey空间里的算子有界性

Let G be a locally compact Vilenkin group. We will establish the boundedness in Morrey spaces L^p,λ(G) for a large class of sublinear operators and linear commutators.     

K -- Convex Operators and Walsh Type Norms

A celebrated result of G. Pisier states that the notions of B-convexity and K-convexity coincide for Banach spaces. We complement this in the setting of linear and bounded operators between Banach spaces. Our approach is local and even yields inequalities between gradations of K-convexity norms and Walsh type norms of operators. Our method combines G. Pisier's original ideas and the main steps in the proof of the Beurling-Kato theorem on extensions of C₀-semigroups of operators to holomorphic semigroups with the technique of ideal norms.     

一类次线性算子在局部紧Vilenkin群上Herz型Hardy空间上的有界性

设 G是局部紧的 Vilenkin群 .本文研究了一类具有分数次积分性质的次线性算子从 H Kα,p1q1(G)到 (弱 ) H Kα,p2q2 (G)有界的判别条件 .     

LOCAL HARDY SPACES ON HEISENBERG GROUP OVER LOCAL FIELDS

ＬＯＣＡＬＨＡＲＤＹＳＰＡＣＥＳＯＮＨＥＩＳＥＮＢＥＲＧＧＲＯＵＰＯＶＥＲＬＯＣＡＬＦＩＥＬＤＳ￥ＺｈｏｕＧｕａｎｇｃａｉ（周广才）（Ｄｅｐｔ．ｏｆＭａｔｈ．＆Ｍｅｃｈ．，ＳｏｕｔｈｅａｓｔＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００１８，Ｃｈｉｎａ...     

Parametrix constructions for right invariant differential operators on nilpotent groups

Algebras of right invariant pseudo-differential operators are constructed on any graded nilpotent group G . We obtain parametrices in such algebras for right invariant differential operators P such that P and its adjoint satisfy the hypoellipticity condition of Rockland .     

Mixed logic and storage operators

In 1990 J-L. Krivine introduced the notion of storage operators. They are -terms which simulate call-by-value in the call-by-name strategy and they can be used in order to modelize assignment instructions. J-L. Krivine has shown that there is a very simple second order type in AF2 type system for storage operators using G?del translation of classical to intuitionistic logic. In order to modelize the control operators, J-L. Krivine has extended the system AF2 to the classical logic. In his system the property of the unicity of integers representation is lost, but he has shown that storage operators typable in the system AF2 can be used to find the values of classical integers. In this paper, we present a new classical type system based on a logical system called mixed logic. We prove that in this system we can characterize, by types, the storage operators and the control operators. Received: 7 May 1997     

Applications of Automata and Graphs: Labeling-Operators in Hilbert Space I

We show that certain representations of graphs by operators on Hilbert space have uses in signal processing and in symbolic dynamics. Our main result is that graphs built on automata have fractal characteristics. We make this precise with the use of Representation Theory and of Spectral Theory of a certain family of Hecke operators. Let G be a directed graph. We begin by building the graph groupoid $\Bbb{G}$ induced by G, and representations of  $\Bbb{G}$ . Our main application is to the groupoids defined from automata. By assigning weights to the edges of a fixed graph G, we give conditions for $\Bbb{G}$ to acquire fractal-like properties, and hence we can have fractaloids or G-fractals. Our standing assumption on G is that it is locally finite and connected, and our labeling of G is determined by the “out-degrees of vertices”. From our labeling, we arrive at a family of Hecke-type operators whose spectrum is computed. As applications, we are able to build representations by operators on Hilbert spaces (including the Hecke operators); and we further show that automata built on a finite alphabet generate fractaloids. Our Hecke-type operators, or labeling operators, come from an amalgamated free probability construction, and we compute the corresponding amalgamated free moments. We show that the free moments are completely determined by certain scalar-valued functions.