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 \( H : L_p,v → L_q,u, (Hf)(x) := _a^x k(x,t)f(t) dt \) (0.1) with the so-called Oinarov’s kernel \(k(x,t)\) in the weighted Lebesgue spaces \( L_p,v = { f : \|f\|_p,v^p := _a^b |f(t)|^p v(t) dt < ∞ } \) and \( L_q,u = { f : \|f\|_q,u^q := _a^b |f(t)|^q u(t) dt < ∞ } \), in the case \(1 < q < p < ∞\).