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The Dirichlet Space and Related Function Spaces
Mathematical Surveys and Monographs, 2019The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces ...
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Weighted composition operators on the Dirichlet space: boundedness and spectral properties
Mathematische Annalen, 2015Boundedness of weighted composition operators $$W_{u,\varphi }$$Wu,φ acting on the classical Dirichlet space $$\mathcal {D}$$D as $$W_{u,\varphi }f= u\, (f\circ \varphi )$$Wu,φf=u(f∘φ) is studied in terms of the multiplier space associated to the symbol $
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