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 ; the role of boundary is played by a nilpotent (Iwasawa) group of isometries of *M*. For forms satisfying certain 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 , and exhibit explicit isomorphisms between spaces of forms on *M* and the ordinary spaces of functions on the group .

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DOI:
https://doi.org/10.1090/S0002-9947-1977-0477174-1

Article copyright:
© Copyright 1977
American Mathematical Society