Resumen de Interpolation and sampling in small Bergman spaces

Kristian Seip

• 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.