For flat symmetric spaces, L1-L2 dichotomy holds for all rank 1 cases except Cartan type AI, and holds at regular points in SU(2,q) and SU(3,q) but fails at certain singular points in SU(2,q).
’The smoothness of or bital measures on noncompact symmetric spaces, J
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On $L^1$-$L^2$ dichotomy for flat symmetric spaces
For flat symmetric spaces, L1-L2 dichotomy holds for all rank 1 cases except Cartan type AI, and holds at regular points in SU(2,q) and SU(3,q) but fails at certain singular points in SU(2,q).