Boundedness of Integral Operators With Kernels From the Class On±ν,μ, n ≥ 0, in Lebesgue Spaces With Measures

In recent years, weighted inequalities for quasilinear integral operators with iterative structures have been extensively studied. The analysis reduces these inequalities to the study of Volterra operators with increasingly complex kernels and measures. This paper introduces a broader class of kernels, extending existing conditions. Key properties of these kernels are explored, and new boundedness criteria for the corresponding operators in weighted Lebesgue spaces are established. These results provide a foundation for solving inequalities involving quasilinear integral operators and have applications in the analysis of bilinear operators.