AN INTEGRAL INEQUALITY FOR CLASS OF FUNCTIONS IN Fₘ(Ω)

Abstract

In this article, we prove an extensive inequality of Cegrell from class of functions in 𝓕(Ω) to class of functions in Fₘ(Ω). More precisely, we prove that if u₁,…,uₘ ∈ Fₘ(Ω) then ∫Ω𝐻𝑚(𝑢1,...,𝑢𝑚)≤[∫Ω𝐻𝑚(𝑢1)]1/𝑚⋯[∫Ω𝐻𝑚(𝑢𝑚)]1/𝑚.∫ Ω H m(u 1,...,u m )≤[∫ Ω H m(u 1​)] 1/m ⋯[∫ Ω H m(u m)] 1/m .