Alternative criteria for the boundedness of volterra integral operators in lebesgue spaces

Three different criteria for Lp -Lq boundedness of Volterra integral operator (1.1) with locally integrable weight functions w, v and a non-negative kernel k(x,y) satisfying Oinarov's condition for each case 1 < p ≤ q < ∞ and 1 < q < p < ∞ are given. Relations between components of the boundedness constants are described.