The role of BMOA in the boundedness of weighted composition operators |
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| Authors: | Eva A. Gallardo-Gutié rrez,Jonathan R. Partington |
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| Affiliation: | a Departamento de Matemáticas, Universidad de Zaragoza e IUMA, Plaza San Francisco s/n, 50009 Zaragoza, Spain
b School of Mathematics, University of Leeds, Leeds LS2 9JT, UK |
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| Abstract: | Boundedness (resp. compactness) of weighted composition operators Wh,φ acting on the classical Hardy space H2 as Wh,φf=h(f○φ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and φ whenever h∈BMOA (resp. h∈VMOA). Analogous results are given for Hp spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space). |
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| Keywords: | Weighted composition operators BMOA and VMOA Nevanlinna counting functions |
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