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Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball (1601.03031v2)
Published 12 Jan 2016 in math.CV
Abstract: We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces $Hp(\mathbb B)$ and the Bergman spaces $\mathcal Ap(\mathbb B)$ of the quaternionic unit ball $\mathbb B$. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudohyperbolic balls is not possible.