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

Ioann Vasilyev

Published 2024-02-19, updated 2024-05-20Version 2

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 $j=1,\ldots, n$. Here, $R_1,\ldots, R_n$ are the Riesz transformations.