Abstract
Sufficient conditions for the compactness in generalized Morrey spaces of the composition of a convolution operator and the operator of multiplication by an essentially bounded function are obtained. Very weak conditions on the function are also obtained under which the commutator of the operator of multiplication by such a function and a convolution operator is compact. The compactness of convolution operators in domains of cone type is investigated.
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Dedicated to the blessedmemory of Nikolai Karapetovich Karapetyants
Original Russian Text © O. G. Avsyankin, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 3, pp. 336–344.
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Avsyankin, O.G. Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces. Math Notes 104, 331–338 (2018). https://doi.org/10.1134/S000143461809002X
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DOI: https://doi.org/10.1134/S000143461809002X