调和分析中的内插定理
Interpolation Theorems in Harmonic Analysis
摘要：
本文主要研究了四个内插定理，并提供了必要的背景资料和一些应用。在第一章的前三节中介绍的材料被用来激发和证明Riesz-Thorin内插定理及其由Stein推广，这两个定理都在第四节中给出。第2章围绕卡尔德龙的复杂的插值方法和内插定理的费曼和斯泰因，与材料之间提供必要的例子和工具。这两个定理，然后应用到一个简短的研究线性偏微分方程，索伯列夫空间，和傅里叶积分算子，提出了在第二章的最后一节。
英文摘要：
This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the Riesz-Thorin interpolation theorem and its extension by Stein, both of which are presented in the fourth section. Chapter 2 revolves around Calderón's complex method of interpolation and the interpolation theorem of Fefferman and Stein, with the material in between providing the necessary examples and tools. The two theorems are then applied to a brief study of linear partial differential equations, Sobolev spaces, and Fourier integral operators, presented in the last section of the second chapter.
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