牛顿Lorentz度量空间
Newtonian Lorentz Metric Spaces
摘要：
本文研究了牛顿Sobolev-Lorentz空间。我们证明了这些空间是Banach空间。我们还研究了可求长曲线族的整体p，q-容度和p，q-模。在一些额外的假设下（即空间带有一个加倍测度和一个弱Poincare不等式），以及对q的一些限制，我们证明了Lipschitz函数在这些空间中是稠密的.此外，在相同的设置，我们表明，p，q-容量是Choquet提供的q是严格大于1。我们还提供了一个反例的密度结果的Lipschitz函数在欧几里德设置时，q是无限的。
英文摘要：
This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p,q-capacity and the p,q-modulus of families of rectifiable curves. Under some additional assumptions (that is, the space carries a doubling measure and a weak Poincare inequality) and some restrictions on q, we show that the Lipschitz functions are dense in those spaces. Moreover, in the same setting we show that the p,q-capacity is Choquet provided that q is strictly greater than 1. We also provide a counterexample to the density result of Lipschitz functions in the Euclidean setting when q is infinite.
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