We generalize the results of [11] and [12] for the unit ball of ℂ d . In particular, we show that under the weight condition (B) the weighted H ∞-space on 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 ℂ d . In addition, we show that for the polydisc d , the weighted H ∞-space is never isomorphic to ℓ∞.
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机译：我们将ℂ d 的单位球的结果推广到[11]和[12]。特别是，我们证明了在加权条件（B）下，加权的H ∞-空间on与ℓ∞同构，因此与相应的加权L 互补∞-空间。我们相应地构造了具体的广义Bergman投影。我们还考虑了域为整个空间ℂ d 的情况。另外，我们表明，对于多碟 d ，加权H ∞空间从不与ℓ∞同构。
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