Characterization of generalized Orlicz spaces

Rita Ferreira, Peter Hästö, Ana Margarida Ribeiro

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

Original languageEnglish
JournalCommunications in Contemporary Mathematics
DOIs
Publication statusE-pub ahead of print - 26 Nov 2018

Keywords

  • Musielak-Orlicz spaces
  • Orlicz space
  • Poincaré inequality
  • Sobolev space
  • variable exponent

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