A remark on irregularity of the -Neumann problem on non-smooth domains

It is an observation due to J. J. Kohn that for a smooth bounded pseudoconvex domain in there exists such that the -Neumann operator on maps (the space of -forms with coefficient functions in -Sobolev space of order ) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex domain in , smooth except at one point, whose -Neumann operator is not bounded on for any .

     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Dolbeault complex in infinite dimensions I

In this paper we introduce certain basic notions concerning infinite dimensional complex manifolds, and prove that the Dolbeault cohomology groups of infinite dimensional projective spaces, with values in finite rank vector bundles, vanish. Some applications of such vanishing theorems are discussed; e.g., we classify vector bundles of finite rank over infinite dimensional projective spaces. Finally, we prove a sharp theorem on solving the inhomogeneous Cauchy-Riemann equations on affine spaces.

     

The complex Hessian equation with infinite Dirichlet boundary value

The existence and nonexistence of the -subharmonic solutions for the complex Hessian equations with infinite Dirichlet boundary value are proved in the certain bounded domain in . We calculate the k-Hessian of the radially symmetric function and use radial functions to construct various barrier functions in this paper. Moreover, it is shown that the growth rate conditions are nearly optimal.

     

Long-Time Asymptotics of Complex mKdV Equation with Weighted Sobolev Initial Data

In this paper, we apply $\bar{\partial}$-steepest descent method to analyze the long-time asymptotics of complex mKdV equation with the initial value belonging to weighted Sobolev spaces. Firstly, the Cauchy problem of the complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering data. Then the long-time asymptotics of complex mKdV equation is obtained by studying the solution of the Riemann-Hilbert problem.     

The Dolbeault complex in infinite dimensions III. Sheaf cohomology in Banach spaces

We prove that the sheaf cohomology groups H ^q (Ω,?) vanish if Ω is a pseudoconvex open subset of a Banach space with unconditional basis, and q≥1. Oblatum 23-XII-1999 & 12-V-2000?Published online: 16 August 2000     

{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces

Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$.     

Complemented isometric copies of in dual Banach spaces

Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .

     

Orlicz范数下的Hardy-Hilbert不等式

给出了Orlicz范数下的Hardy-Hilbert不等式的一种形式,建立了当N-函数M(u)及其余N-函数N(u)均满足Δ′条件时Orlicz范数下的积分型及双级数型Hardy-Hilbert不等式.     

The structure of measurable mappings with values in locally convex spaces

The purpose of this paper is to show that a theorem of A. Wisniewski remains valid without the approximation property.

     

Cesàro function spaces fail the fixed point property

The Cesàro sequence spaces , are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesàro function spaces on both and for are not reflexive and they fail to have the fixed point property.

     

基于完备BR0-代数的全蕴涵三I算法

研究了基础$BR_0$-代数的性质和基于完备基础$BR_0$-代数的全蕴涵三I算法,对一般蕴涵算子给出了三I算法解存在的一个充分条件,并将结果应用于$R_0$-单位区间$\overline{W}$,不但极大的简化了$R_0$-单位区间$\overline{W}$的$R_0$-型$\alpha$-三I算法结果的证明,而且使其证明过程与相应的模糊命题演算系统结合起来,说明了$R_0$-型三I算法是与$B{\cal L}^*$系统相匹配的模糊推理方法.     

The canonical solution operator to restricted to Bergman spaces

We first show that the canonical solution operator to restricted to -forms with holomorphic coefficients can be expressed by an integral operator using the Bergman kernel. This result is used to prove that in the case of the unit disc in the canonical solution operator to restricted to -forms with holomorphic coefficients is a Hilbert-Schmidt operator. In the sequel we give a direct proof of the last statement using orthonormal bases and show that in the case of the polydisc and the unit ball in 1,$"> the corresponding operator fails to be a Hilbert-Schmidt operator. We also indicate a connection with the theory of Hankel operators.

     

一般化凸空间上的变分不等式解的存在性问题

在本文,我们首先给出了KKM型定理和择一定理,然后根据上述结果讨论了一 般化凸空间上变分不等式解的存在性问题.     

Irreducible representations of the Cuntz algebra

In this paper, we establish formulas for the configuration of a special class of irreducible representations of the Cuntz algebra , . These irreducible representations arise as subrepresentations of naturally occurring representations of acting in and arise from consideration of multiresolution wavelet filters.

     

关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记

D.M. Speegle 在文献[1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in [0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献[1] 的注解.     

A Banach space with a countable infinite number of complex structures

We give examples of real Banach spaces with exactly infinite countably many complex structures and with _ω1${\omega }_1$ many complex structures.     

The convergence-extension theorem of Noguchi in infinite dimensions

In this note we give generalizations of Noguchi's convergence-extension theorem to the case of infinite dimension.