L^p（E）（1〈p〈∞）的自反性的一个构造性证明

给出了L^p（E）（1〈p〈∞）的自反性的一个构造性证明．     

Generalized area operators on L^p（R^n）

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces R＋^n＋1. The characterization of the boundedness and compactness of the generalized area operator from LP（]Rn） to Lq（IRn） is investigated in terms of s-Carleson measures with 1 〈 p, q 〈 ＋∞. In the case of p = q = 1, the weak type estimate is also obtained.     

双线性型Hardy算子

介绍了一类双线性型加权Hardy算子,对于p, p1, p2∈[1,∞],证明了Hardy算子是映L^p1 × L^p2 2到Lp有界的。     

A Class of Maximal Functions with Oscillating Kernels

The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.     

Lp空间有理插值型算子的逼近

考虑了两类有理插值型算子的Jackson型估计．当p〉1时．建立了Dilzian—Totik型定理，当p=1时．利用通常连续模给出了Jackson型估计．     

$ L^p $-Theory of the Stokes equation in a half space

In this paper, we investigate -estimates for the solution of the Stokes equation in a half space H where . It is shown that the solution of the Stokes equation is governed by an analytic semigroup on or . From the operatortheoretical point of view it is a surprising fact that the corresponding result for does not hold true. In fact, there exists an -function f satisfying such that the solution of the corresponding resolvent equation with right hand side f does not belong to . Taking into account however a recent result of Kozono on the nonlinear Navier-Stokes equation, the -result is not surprising and even natural. We also show that the Stokes operator admits a R-bounded -calculus on for 1 < p < and obtain as a consequence maximal -regularity for the solution of the Stokes equation. Received August 24, 2000; accepted September 30, 2000.     

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lpspaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H∞functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.     

Lp空间中无限能量的Vlasov-Poisson-Fokker-Planck方程

本文主要研究具有无限能量的Vlasov-Poisson-Fokker-Planck方程,当初值属于Lp空间时,我们给出了方程整体解的存在性证明.     

Spaces of type and the Hankel convolution

In this paper we introduce new function spaces that are denoted by , -1/2$"> and and that are spaces of type where the Hankel convolution and the Hankel transformation are defined. The spaces will play the same role in the Hankel setting that the spaces play in the theory of Fourier transformation.     

非交换L^p（M；τ）空间中有关连加和及直和的一些不等式

证明了一些有关广义奇异值的不等式和非交换L^p（M;τ）空间中的一些不等式．