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

Ioann Vasilyev

paper

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

arXiv:2402.12582

Abstract

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.

arXiv comment8 pages, no figures; typos in the Abstract corrected

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

Abstract

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