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 by 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 homogeneous kernel and bounded characteristic.