On the compactness of convolution-type operators in Morrey spaces

In a Morrey space, the product of the convolution operator with summable kernel and the operator of multiplication by an essentially bounded function is considered. Sufficient conditions for such a product to be compact are obtained. In addition, it is shown that the commutator of the convolution operator and the operator of multiplication by a function of weakly oscillating type is compact in a Morrey space.