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DMV-PTM Mathematical Meeting 17–20.09.2014, Pozna´n

GENERALIZED HILBERT OPERATORS

Petros Galanopoulos

Aristotle University of Thessaloniki Department of Mathematics, Greece petrosgala@math.auth.gr

The talk is based on the joint work with Daniel Girela, Jose Angel Pelaez and Aristomenis Siskakis

Session: Spaces of Analytic Functions

If g is an analytic function in the unit disc D, we consider the generalized Hilbert operator Hgdefined by

Hg(f )(z) = Z 1

0

f (t)g0(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 Hg is bounded (compact) on the Hardy spaces Hp, the weighted Bergman spaces Apα or on the spaces of Dirichlet type Dpα.

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