Difference norms for vector-valued Bessel potential spaces with an application to pointwise multipliers

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Abstract

In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are RR-boundedness results for Fourier multiplier operators, which are of independent interest. As an application we characterize the pointwise multiplier property of the indicator function of the half-space on these spaces. All results are proved in the setting of weighted spaces.
Original languageEnglish
Pages (from-to)1435-1476
Number of pages42
JournalJournal of Functional Analysis
Volume272
Issue number4
DOIs
Publication statusPublished - 2017

Keywords

  • Difference norm
  • Pointwise multiplier
  • R-boundedness of Fourier multipliers
  • UMD space-valued Bessel potential space

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