Vector-Valued John–Nirenberg inequalities and vector-valued mean oscillations characterization of BMO

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Abstract

We establish a vector-valued John–Nirenberg inequality for oscillations measured in a Banach function space (B.f.s.) norm. This inequality generalizes several existing results on John–Nirenberg inequalities on function spaces such as rearrangement-invariant B.f.s. and Lebesgue spaces with variable exponents. Moreover, this inequality also offers a new characterization of BMO in terms of the weighted vector-valued mean oscillation. Copyright © 2015 Springer Basel.
Original languageEnglish
Pages (from-to)257-270
JournalResults in Mathematics
Volume70
Issue number1-2
Early online dateJul 2015
DOIs
Publication statusPublished - Sep 2016

Citation

Ho, K.-P. (2016). Vector-Valued John–Nirenberg inequalities and vector-valued mean oscillations characterization of BMO. Results in Mathematics, 70(1-2), 257-270.

Keywords

  • John–Nirenberg inequalities
  • Bounded mean oscillation
  • Vector-valued inequalities
  • Banach function spaces
  • Extrapolation
  • 42B35
  • 46E30
  • 42B25

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