INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS OF DEGREE \(\alpha\) IN LEBESGUE SPACES

We consider multidimensional integral operators with homogeneous kernels of degree \(\alpha\) $\alpha$ . We obtain the conditions for \(\alpha\) $\alpha$ , which are necessary for the boundedness of these operators in Lebesgue spaces. Using the conditions for \(\alpha\) $\alpha$ , we establish sufficient conditions for the boundedness of integral operators with homogeneous kernels in Lebesgue spaces. In addition, concrete examples of operators are considered in this paper.