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Gaussian Capacity Analysis

  • Liguang Liu
  • Jie Xiao
  • Dachun Yang
  • Wen Yuan
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2225)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 1-18
  3. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 19-35
  4. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 37-53
  5. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 55-64
  6. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 65-82
  7. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 83-101
  8. Back Matter
    Pages 103-108

About this book

Introduction

This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality.  Applications to function spaces and geometric measures are also presented.

This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.  

Keywords

Gaussian Measure Gaussian Sobolev Function Gaussian BV Function Poincaré Inequality Gaussian Isoperimetry

Authors and affiliations

  • Liguang Liu
    • 1
  • Jie Xiao
    • 2
  • Dachun Yang
    • 3
  • Wen Yuan
    • 4
  1. 1.School of MathematicsRenmin University of ChinaBeijingChina
  2. 2.Department Mathematics & StatisticsMemorial UniversitySt. John’s, Newfoundland and LabradorCanada
  3. 3.Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  4. 4.Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical SciencesBeijing Normal UniversityBeijingChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-95040-2
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-95039-6
  • Online ISBN 978-3-319-95040-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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