The property $\log(f) \in BMO(\mathbb R^n)$ in terms of Riesz transforms

The condition mentioned in the title is equivalent to the representability of $f$ as the quotient $f = v_{1} / v_{2}$ , where $v_{1}$ and $v_{2}$ obey the inequalities $∣ R_{j} v_{i} ∣ \leq C ∣ v_{i} ∣$ for $i = 1, 2$ and $j = 1, \dots, n$ . Here, $R_{1}, \dots, R_{n}$ are the Riesz transformations.

The property $\log (f) \in B M O (R^{n})$ in terms of Riesz transforms

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The property $\log (f) \in B M O (R^{n})$ in terms of Riesz transforms

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The property log⁡(f)∈BMO(Rn)log(f)∈BMO(Rn) in terms of Riesz transforms

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The property log⁡(f)∈BMO(Rn)log(f)∈BMO(Rn) in terms of Riesz transforms

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The property $\log (f) \in B M O (R^{n})$ in terms of Riesz transforms

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The property $\log (f) \in B M O (R^{n})$ in terms of Riesz transforms

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