Integral analog of one generalization of the Hardy inequality and its applications - Mulyava, O. M. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
Under certain conditions on continuous functions μ, λ, a, and f, we prove the inequality _0^y μ (x)λ (x)f( _0^x λ (t)a(t)dt _0^x λ (t)dt )dx K_0^y μ (x)λ (x)f(a(x)) dx, y ∞ , and describe its application to the investigation of the problem of finding conditions under which Laplace integrals belong to a class of convergence.