Fourier multiplier theorems on Besov spaces under type and cotype conditions

Jan Rozendaal, Mark Veraar

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


In this article, we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents p and q, which depend on the type p and cotype q of the underlying Banach spaces. In a previous article, we considered Lp-Lq multiplier theorems. In the current article, we show that in the Besov scale one can obtain results with optimal integrability exponents. Moreover, we derive a sharp result in the Lp-Lq setting as well. We consider operator-valued multipliers without smoothness assumptions. The results are based on a Fourier multiplier theorem for functions with compact Fourier support. If the multiplier has smoothness properties, then the boundedness of the multiplier operator extrapolates to other values of p and q for which 1/p - 1/q remains constant.

Original languageEnglish
Pages (from-to)713-743
Number of pages31
JournalBanach Journal of Mathematical Analysis
Issue number4
Publication statusPublished - 2017


  • Besov spaces
  • Extrapolation
  • Fourier type
  • Operator-valued Fourier multipliers
  • Type and cotype


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