New atomic decompositons for Bergman spaces on the unit ball

Jens Christensen; Karlheinz Gröchenig; Gestur Ólafsson

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arXiv · 1504.00381

New atomic decompositons for Bergman spaces on the unit ball

Jens Christensen·Karlheinz Gröchenig·Gestur Ólafsson

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Abstract

We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast to our predecessors, we use group theoretic methods, in particular the representation theory of the discrete series of $SU(n,1)$ and its covering groups. One of the benefits is a much larger class of admissible

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Jens Christensen, Karlheinz Gröchenig, Gestur Ólafsson. 2015-04-01. New atomic decompositons for Bergman spaces on the unit ball. https://arxiv.org/abs/1504.00381

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