Title: Scaling invariant Sobolev-Lorentz capacity on $\mathbb{R}^{n}$

Authors: Serban Costea

Issue: Volume 56 (2007), Issue 6, 2641-2670

Abstract: We develop a capacity theory based on the definition of Sobolev functions on $\mathbf{R}^n$ with respect to the Lorentz norm. Basic properties of capacity, including monotonicity, finite subadditivity and convergence results are included. We also provide sharp estimates for the capacity of balls. Sobolev-Lorentz capacity and Hausdorff measures are related.