Loeb乘积空间及Keisler′s Fubini定理

在非标准多饱和模型下,研究了Loeb乘积空间及Keisler′s Fubini定理.首先,应用Loeb构造方法分别构造了Loeb乘积空间L(Y1×Y2)和乘积Loeb空间L(Y1)×L(Y2),并得到了L(A1)×L(A2)L(A1×A2).其次,A∈L(A1×A2),证明了如果(ν1×ν2)L(A)=0,则对于几乎所有的y1∈Y1,截口Ay1是L(A2)-可测的.最后,在Loeb乘积空间上证明了Keisler′s Fubini定理.

A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

利用重积分求解一元积分

对于一些难以求解的一元积分,可以将被积函数或者被积函数中的一部分转化为另外一个定积分或者广义积分,这样就将一元定积分变成了多元函数的重积分,再通过交换积分顺序就可以得到原积分的结果.以几个典型的积分为例,利用这种方法,最终求得积分结果.

Hardy型算子的一些端点估计

首先,研究一维Hardy型算子的一些端点估计;其次,利用Fubini定理与球面坐标变换研究了高维Hardy型算子的相应端点估计;最后,通过构造特例证明了Hardy型算子的这些端点估计对某些指标限制的必要性,扩展和改进了现有的一些结论。