Gaussian capacity analysis
type: Item
instance of: scholarly article
title: Gaussian capacity analysis
zbMATH Open document ID: 1412.60004
DOI: 10.1007/978-3-319-95040-2
author: Jie Xiao
author: Wen Yuan
author: Li Guang Liu
author: Dachun Yang
published in: Lecture Notes in Mathematics
publication date: 2018-07-19T00:00:00Z
review text: From the cover of the 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.\par This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.''\par In the Preface you can read: ``This monograph is a new development of the geometric potential analysis based on the Gaussian space.'''\par The book is very large structured in a Preface, 6 chapters (divided in 19 subchapters), Bibliography and Index:\par Chapter 1. Gaussian Sobolev $p$-space -- Chapter 2. Gaussian Campanato $(p, t)$-class -- Chapter 3. Gaussian $p$-capacity -- Chapter 4. Restriction of Gaussian Sobolev $p$-space -- Chapter 5. Gaussian 1-capacity to Gaussian $\infty$-capacity -- Chapter 6. Gaussian BV-capacity.\par Every chapter starts with a short introduction on the aim of the chapter followed by some subchapters. The Bibliography contains 59 references, the index about 40 items and a list of the used about 50 symbols.\par The book can be recommend all readers, who are interested in this field.
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 6908789
zbMATH Keywords: Gaussian Poincaré $p$-inequality
zbMATH Keywords: Lebesgue volume element
zbMATH Keywords: Gauss space $C^n$
zbMATH Keywords: Campanato space
zbMATH Keywords: Gaussian $p$-capacity
zbMATH Keywords: Gaussian volume element
zbMATH Keywords: canonical Gaussian measure density
zbMATH Keywords: continuous functions with compact support in $\mathbb{R}^n$
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-95040-2
OpenAlex ID: W2891211100
description: scientific article; zbMATH DE number 6908789