Some new iterated hardy-type inequalities: The case θ= 1

الأصل · EN

In this paper we characterize the validity of the Hardy-type inequality equation* ∫ₛ∞h(z)dzₚ,ᵤ,₍₀,ₜ₎q,w,∞≤ c h₁,ᵥ,∞ equation* where 0<p< ∞, 0<q≤ +∞, u, w and v are weight functions on (0,∞). It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardy-type operators restricted to the cone of monotone functions and for the generalized Stieltjes operator.