Resumen de Improving multipliers and zero sets in \mathcal {Q}_K spaces

Guanlong Bao, Zengjian Lou, Ruishen Qian, Hasi Wulan

• Let ? and ? be two spaces of analytic functions in the unit disk ? with ?⊆? . An inner function ? is said to be (?,?) -improving if ??∈? whenever ?∈? and ??∈? . Under mild conditions on the weight function ? , we prove that inner functions in ? are precisely the ones which are (?,????) -improving and (?,) -improving. Meanwhile, the zero sets in ? spaces are determined in terms of Carleson–Newman sequences.