Resumen de Scaling invariant Sobolev-Lorentz capacity on $\mathbb{R}^{n}$

Serban Costea

• We develop a capacity theory based on the definition of Sobolev functions on Rn 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.