Abstract
Recently Choe et al. have introduced the notion of dual Berezin transforms and used it to obtain new characterizations of the Carleson measures for the weighted Bergman spaces over the unit ball in C n. Continuing our investigation on the Hardy spaces, we obtain new characterizations of the Carleson measures for the Hardy spaces by means of the dual Poisson–Szegö transforms introduced by Koosis. Compared with the results for the weighted Bergman spaces, our results for the Hardy spaces not only show an similarity, but also reveal a new characterization.
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In memory of Professor Walter Rudin.
The first and third authors were supported by Mid-career Researcher Program through NRF grant funded by the MEST(R01-2008-000-20206-0).
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Choe, B.R., Izuchi, K.H. & Koo, H. Hardy–Carleson Measures and Their Dual Poisson–Szegö Transforms. Potential Anal 38, 143–168 (2013). https://doi.org/10.1007/s11118-011-9268-3
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DOI: https://doi.org/10.1007/s11118-011-9268-3