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Journal of Lie Theory 18 (2008), No. 1, 181--191
Copyright Heldermann Verlag 2008

The Dual of Kawazoe's Atomic Hardy Space H1p,0

Andreas Nilsson
SAAB Aerosystems, Bröderna Ugglas Gata, 58188 Linköping, Sweden

The purpose of this paper is to determine the dual of Kawazoe's atomic Hardy space for semisimple Lie groups. The conclusion is that it consists of functions, whose translates satisfy conditions which are similar to the conditions for Goldberg's Euclidean local bmo-space. We will also find the duals of the corresponding K-invariant and K-bi-invariant spaces.

Keywords: Hardy space, BMO, semisimple Lie group.

MSC: 43A15; 22E30

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