Schatten $p$ class commutators on the weighted Bergman space $L^2 _a (\mathbb{B}_n, dv_\gamma)$ for $\frac{2n}{n + 1 + \gamma} < p < \infty$} Joshua Isralowitz 47B3547B38Schatten classescommutatorsHankel operators Let $P_{\gamma}$ be the orthogonal projection from the space $L^2(\mathbb{B}_n,\mathrm{d}v_{\gamma})$ to the standard weighted Bergman space $L_a^2(\mathbb{B}_n,\mathrm{d}v_{\gamma})$. In this paper, we characterize the Schatten $p$ class membership of the commutator $[M_f,P_{\gamma}]$ when $2n/(n+1+\gamma)<p<\infty$. In particular, we show that if $2n/(n+1+\gamma)<p<\infty$, then $[M_f,P_{\gamma}]$ is in the Schatten $p$ class if and only if the mean oscillation $\operatorname{MO}_{\gamma}(f)$ is in $L^p(\mathbb{B}_n,\dtau)$ where $\dtau$ is the M\"obius invariant measure on $\mathbb{B}_n$. This answers a question recently raised by K. Zhu. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4767 10.1512/iumj.2013.62.4767 en Indiana Univ. Math. J. 62 (2013) 201 - 233 state-of-the-art mathematics http://iumj.org/access/