LOWER BOUNDS ON LP QUASI‐NORMS AND THE UNIFORM SUBLEVEL SET PROBLEM

Recently, Steinerberger (Potential Analysis, 2020) proved a uniform inequality for the Laplacian serving as counterpoint to standard sublevel set which is known fail Laplacian. In this paper, we observe that many inequalities of type follow from lower bound on L1 norm, and give an analogous result any linear differential operator, can non-linear operators. We consider bounds L p quasi-norms < 1 stronger property remains weaker than prove heat conclude with some naturally arising questions.