On weighted spaces of holomorphic functions of several variables

Abstract

We generalize the results of [11] and [12] for the unit ball \( \mathbb{B}_d \) of ℂd. In particular, we show that under the weight condition (B) the weighted H∞-space on \( \mathbb{B}_d \) is isomorphic to l∞ and thus complemented in the corresponding weighted L∞-space. We construct concrete, generalized Bergman projections accordingly. We also consider the case where the domain is the entire space ℂd. In addition, we show that for the polydisc \( \mathbb{D}^d \)d, the weighted H∞-space is never isomorphic to l∞.