Composition operators on weighted spaces of holomorphic functions on the upper half plane

• Wolfgang Lusky ^[1]
  1. [1] University of Paderborn

     University of Paderborn

     Kreis Paderborn, Alemania

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 122, Nº 1, 2018, págs. 141-150
• Idioma: inglés
• DOI: 10.7146/math.scand.a-97126
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider moderately growing weight functions v on the upper half plane G called normal weights which include the examples (Imw)a, w∈G, for fixed a>0. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators Cφ on the weighted spaces Hv(G). We characterize those holomorphic functions φ:G→G where the composition operator Cφ is a bounded operator Hv(G)→Hv(G) by a simple property which depends only on φ but not on v. Moreover we show that there are no compact composition operators Cφ on Hv(G).