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Session 33. Spaces of analytic functions
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Generalized Hilbert operators |
Petros Galanopoulos, Aristotle University of Thessaloniki, Greece
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The talk is based on the joint work with Daniel Girela, Jose Angel Pelaez and Aristomenis Siskakis
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If \(g\) is an analytic function in the unit disc \( D\), we consider the generalized Hilbert operator \(H_g\)
defined by
\[ H_g(f)(z)=\int_0^1 f(t)g'(tz) \, dt. \]
We study these operators acting on classical spaces of analytic functions in the unit disc.
More precisely, we address the question of characterizing the function \(g\) for which the operator \(H_g\)
is bounded (compact) on the Hardy spaces \(H^p\), the weighted Bergman spaces \(A_{\alpha}^p\) or on the spaces of Dirichlet type
\(D_{\alpha}^p\).
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