Examples
Examples of BMO functions include the following:
- All bounded (measurable) functions. If f is in L∞, then ||f||BMO≤2||f||∞: however, the converse is not true as the following example shows.
- The function log(|P|) for any polynomial P that is not identically zero: in particular, this is true also for |P(x)|=|x|.
- If w is an A∞ weight, then log(w) is BMO. Conversely, if f is BMO, then eδf is an A∞ weight for δ>0 small enough: this fact is a consequence of the John-Nirenberg Inequality.
Read more about this topic: Bounded Mean Oscillation
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