This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.

Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator $u{C}_{\phi }$ on H() is defined by $u{C}_{\phi }f\left(z\right)=u\left(z\right)f\left(\phi \left(z\right)\right)$. We investigate the boundedness and compactness of $u{C}_{\phi }$ induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.