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 ? 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.