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Lorentz Spaces and Lie Groups

✍ Scribed by E. Tychopoulos

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
490 KB
Volume
84
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper is motivated by the behavior of the heat diffusion kernel p t (x) on a general unimodular Lie group. Indeed, contrary to what happens in R n , the P t (x) on a general Lie group is behaving like t &$(t)Â2 for two possibly distinct integers $(t), one for t tending to 0 and another for t tending to , namely d and D. This forces us to consider a natural generalization of Lorentz spaces with different indices at zero'' and at infinity.'' 1996 Academic Press, Inc. 0.2. Let G be a connected Lie group and g its Lie algebra generated by a Hormander system of left invariant vector fields. We define B t =[x # G: d(x, e)<t], the ball of radius t contered at the point e # G.

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