有界性

In chapter 1, we introduce the definitions of area integral S_β and invariant g-function on unit sphere, and study their boundedness on BMO and non-isotropic Lipschitz spaces.

共分三章，第一章引进了C~n单位球面上的面积积分和不变g函数，研究它们在BMO空间以及non-isotropic Lipschitz空间上的有界性问题。

In chapter 2, we consider the boundedness of the Marcinkiewicz integral operator with rough kernel on the weighted Herz spaces .

在第二章中，我们考虑了带有粗糙核的Marcinkiewicz积分算子在加权Herz空间上的有界性。

In this paper,we consider the Marcinkiewicz integral with rough kernel and prove that is bounded on the weighted Herz space s under certain sufficient conditions.

讨论了一类带有粗糙核的Marcinkiewicz积分算子在加权Herz空间上的有界性。

Basing on thesingular integral operators T with weaker kernel introduced in chapter two,westudy the weighted boundedness on〓(1＜p＜∞)and the endpoint estima-tes of their higher order commutators with BMO functions in chapter three.

对第二章引入的弱核奇异积分算子，第三章主要讨论它们与BMO函数的高阶交换子〓在〓上的有界性及端点估计。

By integral in mean and comparison theorem, boundednesses of consumer population and resources, as well as a sufficient condition for population's weak persistent in mean are given when the environment is with a small capacity.

利用积分均值法和比较定理，给出消费者种群和资源量的有界性，以及环境容量较小情形下种群弱平均持续生存的充分条件。

Chapter 3 is devoted to equistability and equiboundedness of matrix differential equations by making use of the symbol property of the matrix Liapunov function and its Dini derivate on specific set.

第三章研究了矩阵微分方程的渐近行为，给出了直接运用矩阵Liapunov函数在某特定集合上的符号与其广义Dini导数符号的性质研究矩阵微分方程的稳定性和有界性。

Deviate argument; Limit circle case; Limit point case; The boundedness of solutions; Integral inequality

基础科学，数学，数学分析偏差变元；极限圆型；极限点型；有界性；积分不等式

A three solutions theorem of nonlinear operator equation in Hilbert space was given by Sun Jing-xian in 1983,in this paper,the theorem was expanded to general Banach space by using gradient method ,and some conditions was weakened,such as the local Lipschitz condition s transformation to the bounded character of F and so on.

依据H ilbert空间中非线性算子方程的一个三解定理，本文运用最速下降法将这个定理推广到了一般的Banach空间，并且减弱了原定理的某些条件，如将局部Lipschitz条件减弱为F的有界性等

In the meanwhile,we also establish the boundedness results of the higher order commutators generated by Hardy-Littlewood maximal operator with rough kernels and corresponding fractional maximal operator with rough kernels on MK_~.

同时还建立了Hardy-Littlewood极大粗糙算子和相应的分数次极大粗糙算子所生成的高阶交换子在MK_~上的有界性。

In the third chapter, based on the second chapter, we will study the boundedness of fractional intergral operator and maximal fractional operator with rough kernal on the weighted Herz-Morrey space.

在第三章中，我们研究了加权齐次Herz-Morrey空间MK_~(ω_1，ω_2)上另一类算子带粗糙核的分数次极大算子和分数次积分算子的有界性问题。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。