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Hausdorff operators on some spaces of holomorphic functions on the unit disc. (English) Zbl 1494.47087

Summary: We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Approximation of the identity by Hausdorff operators is also considered.

MSC:

47G10 Integral operators
47B38 Linear operators on function spaces (general)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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