Interpolation and sampling in small Bergman spaces

الأصل · EN

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 H² appear naturally as a "degenerate" endpoint case for the class of Bergman spaces under study.