Abstract
Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights (1 − |z|)−α, 0 < α < 1. These results make the Hardy space H 2 appear naturally as a “degenerate” endpoint case for the class of Bergman spaces under study.
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The author is supported by the Research Council of Norway grant 185359/V30. This work was started when the author visited CMI, LATP, Université de Provence in the summer of 2010 and finished when he was a participant in the program Complex Analysis and Spectral Problems at Centre de Recerca Matemàtica, Bellaterra in the summer of 2011. He is grateful to both institutions for their support and hospitality.