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Contractive multipliers from Hardy space to weighted Hardy space


Authors: Joseph A. Ball and Vladimir Bolotnikov
Journal: Proc. Amer. Math. Soc. 145 (2017), 2411-2425
MSC (2010): Primary 30E05, 47A57, 46E22
DOI: https://doi.org/10.1090/proc/13549
Published electronically: February 20, 2017
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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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Additional Information

Joseph A. Ball
Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123
Email: joball@math.vt.edu

Vladimir Bolotnikov
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
Email: vladi@math.wm.edu

DOI: https://doi.org/10.1090/proc/13549
Keywords: Contractive multiplier, Bergman inner function, multiplier interpolation problems
Received by editor(s): March 27, 2012
Published electronically: February 20, 2017
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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