索伯列夫空間

這部專著的研究提出了一個介紹性的特性Banach空間一定弱可微函數實例變量所產生的inconnection與眾多的理論問題,偏微分方程近似理論,以及許多其他領域的純粹數學和應用數學。這些空間有被聯繫到的名字. . Sobolev俄羅斯mathematician晚,雖然他們的起源比他的主要貢獻totheir發展在1930年代晚期。

Preface

Lisf of Spaces and Norms

1. PRELIMINARIES

Notation

Topological Vector Spaces

Normed Spaces

Spaces of Continuous Functions

The Lebesgue Measure in Rn

The Lebesgue Integral

Distributions and Weak Derivatives

2. THE LEBESGUE SPACES Lp(Ω)

Definition and Basic Properties

Completeness of Lp (Ω)

Approximation by Continuous Functions

Convolutions and Young's Theorem

Mollifiers and Approximation by Smooth Functions

Precompact Sets in Lp (Ω)

Uniform Convexity　

The Normed Dual of LP(Ω)

Mixed-Norm Lp Spaces

The Marcinkiewicz Interpolation Theorem

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