在第二章中，作者以谱分解、函数演算等为工具，给出一些重要的算子不等式与范数不等式。
In this chapter, we give some operator inequalities and norm inequalities by means of spectral decomposition and functional calculus.
第二章的内容是算子不等式及范数不等式。
The contents of the second chapter are operator inequalities and norm inequalities.
本文研究高阶复合方程基于能量不等式和生成算子的稠密性。
The proof is based on an energy inequality and the density of the range of the operator generated by the studied problem.
与此同时推广了平行四边形法则，给出了一些重要的算子不等式。
Moreover, the parallelogram law is also generalized and some important operator inequalities are established.
对一类有关圆盘乘子的算子，建立了幂权加权不等式。
Some weighted inequalities with power weights are established for a class of operators related to the disc multiplier.
利用控制不等式理论证明一类算子凸序列不等式，把凸序列不等式推广到算子。
An inequality for convex sequence is proved by means of the control theory, Moreover the inequality established in is generalized.
利用控制不等式理论证明一类算子凸序列不等式，把凸序列不等式推广到算子。
In this paper we prove a class of operator convex sequences inequality by means of the theory of majorization.
作者得到了粗糙核分数次积分算子的两权弱型不等式，推广了Cruz-Uribe和Perez的结果。
The authors give the two-weight weak-type inequality for the rough fractional integral operator, which is an extension of result obtained by Cruz-Uribe and Perez.
作者得到了粗糙核分数次积分算子的两权弱型不等式，推广了Cruz-Uribe和Perez的结果。
The authors give the two-weight weak-type inequality for the rough fractional integral operator, which is an extension of result obtained by Cruz-Uribe and Perez.
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