The role of BMOA in the boundedness of weighted composition operators
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2010
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Elsevier
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Gallardo Gutiérrez, E. A., & Partington, J. R. «The Role of BMOA in the Boundedness of Weighted Composition Operators». Journal of Functional Analysis, vol. 258, n.o 11, junio de 2010, pp. 3593-603. DOI.org (Crossref), https://doi.org/10.1016/j.jfa.2010.02.019.
Abstract
Boundedness (resp. compactness) of weighted composition operators W(h, phi) acting on the classical Hardy space H(2) as W(h, phi) f = h (f o phi) are characterized in terms of a Nevanlinna counting function associated to the symbols h and phi whenever h is an element of BMOA (resp. h is an element of VMOA). Analogous results are given for H(p) 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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Corrigendum to "The role of BMOA in the boundedness of weighted composition operators" [J. Funct. Anal. 258 (11) (2010) 3593–3603] J. Funct. Anal. 259 (2010), no. 10, 2757–2758