Abstract
Let N≥1 and N>1. Let Ω be a domain of ℝN. In this article we shall establish Kato’s inequalities for p-harmonic operators Lp. Here Lp is defined as Lpu=div(|∇u|p−2∇u) for u∈Kp(Ω), where Kp(Ω) is an admissible class. If p=2 for example, then we have Kp(Ω)={u∈Lloc1(Ω):∂ju,∂j,k2u∈Lloc1(Ω) for j,k=1,2,…,N}. Then we shall prove that Lp|u|≥(sgnu)Lpu and Lpu+≥(sgn+u)p−1Lpu in 𝒟′(Ω) with u∈Kp(Ω). These inequalities are called Kato’s inequalities provided that p=2.