On Estimates for Norms of Some Integral Operators with Oinarov's Kernel - Kuliev, Komil (Eurasian Mathematical Journal, 2022)
In this work, we give estimates for the norm of the integral operator \( H : L_{p,v} → L_{q,u}, \quad (Hf)(x) := \int_a^x k(x,t)f(t) \, dt \) \quad (0.1) with the so-called Oinarov's kernel \(k(x,t)\) in the weighted Lebesgue spaces \( L_{p,v} = \left\{ f : \|f\|_{p,v}^p := \int_a^b |f(t)|^p v(t) \, dt < ∞ \right\} \) and \( L_{q,u} = \left\{ f : \|f\|_{q,u}^q := \int_a^b |f(t)|^q u(t) \, dt < ∞ \right\} \), in the case \(1 < q < p < ∞\).