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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Boundary behavior of harmonic forms on a rank one symmetric space


Authors: Aroldo Kaplan and Robert Putz
Journal: Trans. Amer. Math. Soc. 231 (1977), 369-384
MSC: Primary 32M15; Secondary 22E30, 43A85
MathSciNet review: 0477174
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Abstract: We study the boundary behavior of 1-forms on a rank-one symmetric space M satisfying the equations $ d\omega = 0 = \delta \omega $; the role of boundary is played by a nilpotent (Iwasawa) group $ \bar N$ of isometries of M. For forms satisfying certain $ {H^p}$ integrability conditions, we obtain the existence of boundary values in an appropriate sense, characterize these boundary values by means of fractional and singular integral operators on the group $ \bar N$, and exhibit explicit isomorphisms between $ {H^p}$ spaces of forms on M and the ordinary $ {L^p}$ spaces of functions on the group $ \bar N$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0477174-1
PII: S 0002-9947(1977)0477174-1
Article copyright: © Copyright 1977 American Mathematical Society