Gaussian Capacity Analysis

Description

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. Front Matter ....Pages i-ix Gaussian Sobolev p-Space (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 1-18 Gaussian Campanato (p, κ)-Class (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 19-35 Gaussian p-Capacity (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 37-53 Restriction of Gaussian Sobolev p-Space (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 55-64 Gaussian 1-Capacity to Gaussian ∞-Capacity (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 65-82 Gaussian BV -Capacity (Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan)....Pages 83-101 Back Matter ....Pages 103-108