EL-FALLAH, Omar; KELLAY, Karim; KLAJA, Hubert; MASHREGHI, Javad; RANSFORD, Thomas

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EL-FALLAH, Omar
Département de Mathématiques

KELLAY, Karim
Institut de Mathématiques de Bordeaux [IMB]

KLAJA, Hubert
Département de Mathématiques et de Statistiques

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Complex Analysis and Operator Theory. 2015-09-08, vol. 10, n° 1, p. 97-107

Springer Verlag

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Wec onsider Dirichlet spaces with superharmonic weights. This class contains both the harmonic weights and the power weights. Our main result is a characterization of the Dirichlet spaces with superharmonic weights that can be identified as de Branges–Rovnyak spaces. As an application, we obtain the dilation inequality $D_\omega(f_r)≤ \frac{2r}{1+r} D_\omega(f) $ $(0\leq r<1)$, where $D_\omega$ denotes the Dirichlet integral with superharmonic weight $\omega$, and $f_r(z) := f(rz)$ is the r-dilation of the holomorphic function f.< Leer menos

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Dirichlet spaces with superharmonic weights and de Branges-Rovnyak spaces

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