Abstract
We give a necessary and sufficient condition for a measure \(\mu \) in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57–76, 2012). We also provide a simple example showing that the analogue for the Paley–Wiener space does not hold. As it turns out the analogue never holds in any model space.
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First author supported by ANR FRAB: ANR-09-BLAN-0058-02 and CTP network “Analyse mathématique et applications”. Other authors supported by the Generalitat de Catalunya (grants 2009 SGR 01303 and 00420) and the spanish Ministerio de Ciencia e Innovación (projects MTM2011-27932-C02-01 and MTM2011-0374).
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Hartmann, A., Massaneda, X., Nicolau, A. et al. Reverse Carleson measures in Hardy spaces. Collect. Math. 65, 357–365 (2014). https://doi.org/10.1007/s13348-014-0105-z
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DOI: https://doi.org/10.1007/s13348-014-0105-z
Keywords
- Hardy space
- Carleson measure
- Reverse Carleson measure
- Reproducing kernel
- Reproducing kernel thesis
- Model space