We introduce the space of analytic functions on the open unit disk whose derivative has the p-th integrable bounded characteristic on the unit circle. We will give the characterization of a linear isometry of this space. We also characterize the surjective, not necessarily linear, multiplicative isometry of this space.

中文翻译：

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具有 $$N^{p}$$-导数的解析函数空间的等距

我们引入了导数在单位圆上具有第p个可积有界特征的开元圆盘上的解析函数空间。我们将给出这个空间的线性等距的特征。我们还描述了这个空间的满射的，不一定是线性的，乘法等距。