Sharp self-improving properties of generalized orlicz-poincaré inequalities in connected metric measure spaces

Toni Heikkinen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)

Abstract

We study the self-improving properties of generalized φ-Poincaré inequalities in connected metric spaces equipped with a doubling measure. As a consequence we obtain results concerning integrability, continuity and differentiability ofOrlicz-Sobolev functions on spaces supporting a φ-Poincaré inequality. Our results are optimal and generalize some of the results of Cianchi [4, 5], Hajłasz and Koskela [9, 10],MacManus and Pérez [19], Balogh, Rogovin and Zürcher [2] and Stein [22].

Original languageEnglish
Pages (from-to)957-986
Number of pages30
JournalIndiana University Mathematics Journal
Volume59
Issue number3
DOIs
Publication statusPublished - 2010
MoE publication typeA1 Journal article-refereed

Keywords

  • Doubling measure
  • Inequality
  • Metric measure space
  • Orlicz space
  • Poincaré
  • Sobolev embedding differentiability
  • Sobolev space

Fingerprint Dive into the research topics of 'Sharp self-improving properties of generalized orlicz-poincaré inequalities in connected metric measure spaces'. Together they form a unique fingerprint.

Cite this