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Boundary Behavior of Harmonic Forms on a Rank One Symmetric Space

1977
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Transactions of the American Mathematical Society
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We study the boundary behavior of 1-forms on a rank-one symmetric space M satisfying the equations du = 0 = Su; the role of boundary is played by a nilpotent (Iwasawa) group Not isometries of M. For forms satisfying certain Hp 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 N~, and exhibit explicit isomorphisms between Hp spaces of forms on M and

doi:10.2307/1997909
fatcat:4anfvkuacbdwxgq3mtv7zgsley