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Interpolation and sampling in small Bergman spaces (1106.3847v3)
Published 20 Jun 2011 in math.CV and math.FA
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 $(1-|z|){-\alpha}$, $0<\alpha<1$. These results make the Hardy space $H2$ appear naturally as a "degenerate" endpoint case for the class of Bergman spaces under study.
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