半范数(seminorm)是范数的一种推广，其比范数的要求弱（半范数比范数少一个条件：使半范数值为0的元素不一定是0元素），范数一定是半范数。局部凸线性空间的拓扑可以由一族满足分离公理的半范数来确定。
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本文研究索伯·列夫空间半范数的某些性质及其与某类商范数的关系，得到了一些新结果。
In this paper, several properties of seminorm on Sobolev space and its relation to some quotient norm are studied and the new results are obtained.
结论推广了线性算子半群的范数连续性质保持，丰富和完善了非线性算子半群的理论。
The result derived extends persistence of norm continuity of linear strongly continuous semigroups and enriches theory of semigroups of nonlinear operators.
讨论描述希尔伯特空间最终范数连续半群特征的一个算子方程的解，给出这个解的一个显式表达式。
A new perturbation result on the Hilbert space for the eventually norm-continuous semigroups is obtained, which makes the perturbation of the semigroups more abundant.
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