L P-distributions on symmetric spaces
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The notion of L p-distributions is introduced on Riemannian symmetric spaces of noncompact type and their main properties are established. We use a geometric description for the topology of the space of test functions in terms of the Laplace-Beltrami operator. The techniques are based on a-priori estimates for elliptic operators. We show-that structure theorems, similar to ℝn, hold on symmetric spaces. We give estimates for the convolutions.
Mathematics Subject Classification (1991)46F05 46F10 53C21 53C35
Keywordssymmetric spaces Lie groups distributions a- priori estimates
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