On the problem of characterizing multipliers for the Drury-Arveson space Quanlei FangJingbo Xia 46E2247B32.Drury-Arveson spacereproducing kernelmultiplier. Let $H^2_n$ be the Drury-Arveson space on the unit ball $\mathbb{B}$ in $\mathbb{C}^n$, and suppose that $n\geq2$. Let $k_z$, $z\in\mathbb{B}$ be the normalized reproducing kernel for $H^2_n$. In this paper, we consider the following rather basic question in the theory of the Drury-Arveson space: for $f\in H^2_n$, does the condition $\sup_{|z|<1}\|fk_z\|<\infty$ imply that $f$ is a multiplier of $H^2_n$? We show that the answer is negative. We further show that the analogue of the familiar norm inequality $\|H_{\phi}\|\leq C\|\phi\|_{\mbox{\scriptsize BMO}}$ for Hankel operators fails in the Drury-Arveson space. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5506 10.1512/iumj.2015.64.5506 en Indiana Univ. Math. J. 64 (2015) 663 - 696 state-of-the-art mathematics http://iumj.org/access/