LEBLOND, Juliette; POZZI, Elodie; RUSS, Emmanuel

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LEBLOND, Juliette
Analysis and Problems of Inverse type in Control and Signal processing [APICS]

POZZI, Elodie
Institut de Mathématiques de Bordeaux [IMB]

RUSS, Emmanuel
Institut Fourier [IF ]

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Complex Analysis and Operator Theory. 2015, vol. 119, p. 354-381

Springer Verlag

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Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$ on generalized Hardy spaces on $\Omega_2$, recently considered in \cite{bfl, BLRR}. In particular, we provide necessary and/or sufficient conditions on $\phi$, depending on the geometry of the domains, ensuring that these operators are bounded, invertible, isometric or compact. Some of our results are new even for Hardy spaces of analytic functions.< Leer menos

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composition operators

conjugate Beltrami equation

Generalized Hardy spaces

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Composition operators on generalized Hardy spaces

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