Besov spaces and product BMO over polydisc

We prove that the analytic Besov space $B_{p,p}^{1\mathrm{/}p}({\text{C}}_{+}^n)$ embeds continuously into Chang–Fefferman product BMO for every finite $n$ and $1\le p<\mathrm{\infty }$. Consequently, every small Hankel operator in a finite Schatten class has a product BMO symbol. The proof uses smooth product wavelets and an estimate for dyadic rectangles. We also give a condition on Fejér means that yields a BMO symbol for a bounded Hankel operator on the polydisc.