We exhibit the optimal constant for Sobolev inequalities in Lorentz spaces for a mean oscillation, and its relation with a boundedness of the Hardy-Littlewood maximal operator in Sobolev spaces. Some applications to a scale invariant form of Hardy's inequality in a limiting case are also considered.
- Critical Hardy inequalities
- Optimal constant
- Scale invariance property
- Sobolev inequalities in Lorentz spaces