Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups

Autor:	Leonard Gross, Nathaniel Eldredge, Laurent Saloff-Coste
Rok vydání:	2015
Předmět:	Pure mathematics General Mathematics MathematicsofComputing_GENERAL Holomorphic function Mathematics::Analysis of PDEs 01 natural sciences Projection (linear algebra) Sobolev inequality 010104 statistics & probability Mathematics - Analysis of PDEs Mathematics::Probability FOS: Mathematics 0101 mathematics GeneralLiterature_REFERENCE(e.g. dictionaries encyclopedias glossaries) Mathematics Mathematics::Functional Analysis Dirichlet form Mathematics::Complex Variables Applied Mathematics Operator (physics) 010102 general mathematics Probability (math.PR) Lie group 16. Peace & justice Complex Lie group Functional Analysis (math.FA) Mathematics - Functional Analysis 35R03 35H20 43A15 32W30 Hypoelliptic operator Mathematics - Probability Analysis of PDEs (math.AP)
DOI:	10.48550/arxiv.1510.05151
Popis:	We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is strongly hypercontractive in the sense of Janson. This extends previous results of Gross to a setting in which the operator A is not holomorphic. Comment: 46 pages. Minor corrections. To appear in Transactions of the American Mathematical Society
Databáze:	OpenAIRE
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