Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces

Abstract Given measurable functions ϕ, ψ on ℝ + {\mathbb{R}^{+}} and a kernel function k ⁢ ( x , y ) ≥ 0 {k(x,y)\geq 0} satisfying the Oinarov condition, we study the Hardy operator K ⁢ f ⁢ ( x ) = ψ ⁢ ( x ) ⁢ ∫ 0 x k ⁢ ( x , y ) ⁢ ϕ ⁢ ( y ) ⁢ f ⁢ ( y ) ⁢ 𝑑 y , x > 0 , Kf(x)=\psi(x)\int_{0}^{x}k(x,y)\phi(y)f(y)\,dy,\quad x>0, between Orlicz–Lorentz spaces Λ X G ⁢ ( w ) {\Lambda_{X}^{G}(w)} , where f is a measurable function on ℝ + {\mathbb{R}^{+}} . We obtain sufficient conditions of boundedness of K : Λ u 0 G 0 ⁢ ( w 0