Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups

Zoltán M. Balogh, Juan J. Manfredi, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

For a general Carnot group G with homogeneous dimension Q we prove the existence of a fundamental solution of the Q-Laplacian uQ and a constant aQ > 0 such that exp(-aQuQ) is a homogeneous norm on G. This implies a representation formula for smooth functions on G which is used to prove the sharp Carnot group version of the celebrated Moser-Trudinger inequality.

Original languageEnglish (US)
Pages (from-to)35-49
Number of pages15
JournalJournal of Functional Analysis
Volume204
Issue number1
DOIs
StatePublished - Oct 20 2003

Keywords

  • Carnot group
  • Moser-Trudinger inequality
  • Nonlinear potential theory

ASJC Scopus subject areas

  • Analysis

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