ON WEIGHTED BILINEAR INEQUALITY WITH A KERNEL

Introducing a kernel into integral bilinear Hardy-type operators represents a new direction in operator theory. In the general case, since the criterion for the validity of an integral Hardy-type inequality with a kernel in a weighted Lebesgue space is not defined, various conditions are determined on the kernel, and wider results are obtained than in the case without a kernel. This paper examines integral bilinear Hardy-type operators involving the Hardy and Hardy-Volterra operators in weighted Lebesgue spaces. We obtained criteria for the validity of bilinear integral Hardy-type inequalities with kernels in the classes O1+ and O1- for the parameter ranges 1

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