Modular estimates for nonlinear integral operators and applications in fractional calculus

Abstract

Here we give several modular estimates for nonlinear integral operators of the form Tƒ(s) = ∫_{R⁺ N} K (t, s, ƒ(t))dt in Musielak-Orlicz spaces. Moreover, we also furnish a superposition theorem for operators with homogeneous kernels and as applications, we obtain estimates in fractional Musielak-Orlicz spaces.