On the compactness of integral operators with homogeneous kernels in local Morrey spaces

In local Morrey spaces we consider an operator that is the product of a multidimensional integral operator and operators of multiplication by essentially bounded functions. At the same time, we assume that the kernel of the integral operator is homogeneous of degree $(-n)$ and invariant under all rotations. Sufficient conditions are obtained for the compactness of such an operator. We also study the compactness of an operator with a homogeneous kernel and bounded characteristic.