Four Lectures on Real HP Spaces
Four Lectures on Real HP Spaces
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DOI：
10.1142/2650
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发表时间：
1995-05
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影响因子：
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通讯作者：
Shan-zhen Lu
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文献类型：
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作者：
Shan-zhen Lu
这本书介绍了真实的变量理论的HP空间简要和集中在其应用的各个方面的分析领域。全文共分四章。第一章介绍了Führman-Stein关于真实的HP空间的基本理论。第二章介绍了真实的HP空间的原子分解理论和分子分解理论。此外，第二章还讨论了真实的HP空间的对偶空间、HP空间中算子的插值以及HP空间的插值。第三章详细讨论了HP空间中几种基本算子的性质。其中，一些基本结果是中国数学家贡献的，如弱HP空间的分解理论及其在奇异积分尖锐性研究中的应用，HP空间中椭圆Riesz平均的一种新的处理方法，HP乘子的转移定理等。最后一章讨论了真实的HP空间在逼近论中的应用。
This book introduces the real variable theory of HP spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman–Stein on real HP spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real HP spaces. In addition, the dual spaces of real HP spaces, the interpolation of operators in HP spaces, and the interpolation of HP spaces are also discussed in Chapter 2. The properties of several basic operators in HP spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak HP spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in HP spaces, and the transference theorem of HP-multipliers etc. The last chapter is devoted to applications of real HP spaces to approximation theory.