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