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

• Autores: Guanlong Bao, Zengjian Lou, Ruishen Qian, Hasi Wulan
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 3, 2015, págs. 453-468
• Idioma: inglés
• DOI: 10.1007/s13348-014-0113-z
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• Resumen

  • Let X and Y be two spaces of analytic functions in the unit disk \mathbb {D} with X\subseteq Y. An inner function \theta is said to be (X, Y)-improving if f\theta \in X whenever f\in X and f\theta \in Y. Under mild conditions on the weight function K, we prove that inner functions in \mathcal {Q}_{K} are precisely the ones which are (\mathcal {Q}_K, BMOA)-improving and (\mathcal {Q}_K, \mathcal {B})-improving. Meanwhile, the zero sets in \mathcal {Q}_K spaces are determined in terms of Carleson–Newman sequences.