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In this post, a question was raised to discuss the generalization of Sobolev spaces on locally compact Lie groups. Now my question is whether there exists a generalization of Sobolev spaces and associated theories of the Laplace operator on noncompact Lie groups. My expectation is that the theory should be reduced to coincide with that in $\mathbb{R}^n$ as a trivial case of noncompact Lie groups. But I fail to find useful references on this subject. Can someone kindly help me with this difficulty? Thanks in advance.

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  • $\begingroup$ I had a similar question sometime back but could not find anything in literature.. good question. $\endgroup$
    – Creator
    Feb 23, 2016 at 1:51

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