Let $H^p=H^p(B_d)$ denote the Hardy space in the open unit ball $B_d$ of $\mathbb{ C}^d$, $d\ge 1$. We characterize the reverse Carleson measures for $H^p$, $1<p<\infty$, that is, we describe all finite positive Borel measures $\mu$, defined on the closed ball $\overline{ B}_d$, such that \[ \|f \|_{ H^p} \le c \|f\|_{ L^p(\overline{ B}_d,\mu)} \] for all $f\in H^p(B_d) \cap C(\overline{ B}_d)$ and a universal constant $c>0$. Given a non-inner holomorphic function $b: B_d \to B_1$, we obtain properties of the reverse Carleson measures for the de Branges-Rovnyak space $\mathcal{ H}(b)$.
Categories: math.CV