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Gaussian Capacity Analysis

  • Book
  • © 2018

Overview

Authors:
  1. Liguang Liu

    1. School of Mathematics, Renmin University of China, Beijing, China

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  2. Jie Xiao

    1. Department Mathematics & Statistics, Memorial University, St. John’s, Newfoundland and Labrador, Canada

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  3. Dachun Yang

    1. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, China

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  4. Wen Yuan

    1. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, China

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  • The first book presenting a systematic study of the Sovolev/BV capacity theory in the Gaussian setting
  • Provides fundamental material for a cross-disciplinary field
  • Provides interesting applications in the geometry of Gaussian space

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
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  2. Gaussian Sobolev p-Space

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 1-18

  3. Gaussian Campanato (p, κ)-Class

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 19-35

  4. Gaussian p-Capacity

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 37-53

  5. Restriction of Gaussian Sobolev p-Space

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 55-64

  6. Gaussian 1-Capacity to Gaussian ∞-Capacity

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 65-82

  7. Gaussian BV -Capacity

    • Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 83-101

  8. Back Matter

    Pages 103-108
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Keywords

About this book

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. 

Authors and Affiliations

  • School of Mathematics, Renmin University of China, Beijing, China

    Liguang Liu

  • Department Mathematics & Statistics, Memorial University, St. John’s, Newfoundland and Labrador, Canada

    Jie Xiao

  • Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, China

    Dachun Yang, Wen Yuan

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