Contractive multipliers from Hardy space to weighted Hardy space

Ball, Joseph; Bolotnikov, Vladimir

doi:10.1090/proc/13549

Contractive multipliers from Hardy space to weighted Hardy space
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by Joseph A. Ball and Vladimir Bolotnikov PDF

Proc. Amer. Math. Soc. 145 (2017), 2411-2425 Request permission

Abstract:

It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\mathbf {\beta }}$ can be factored as a fixed factor composed with a classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied to get results on interpolation for a Hardy-to-weighted-Hardy contractive multiplier class, as well as a new characterization of Bergman inner functions.

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