### Extensions of the theory of tent spaces and applications to boundary value problems

Alex Amenta
We extend the theory of tent spaces from Euclidean spaces to various types of metric measure spaces. For doubling spaces we show that the usual 'global' theory remains valid, and for 'non-uniformly locally doubling' spaces (including R^n with the Gaussian measure) we establish a satisfactory local theory. In the doubling context we show that Hardy–Littlewood–Sobolev-type embeddings hold in the scale of weighted tent spaces, and in the special case of unbounded AD-regular metric measure spaces...
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