In this paper, we study the compactness of the generalized truncated Riesz potential on various versions of Morrey-type spaces. The main attention is paid to obtaining necessary and sufficient conditions that ensure the compactness of this operator. For this purpose, a detailed analysis of the functional properties of the generalized truncated Riesz potential is carried out, which made it possible to identify exact conditions on the space parameters under which the operator is compact. In particular, theorems are proved that establish a relationship between the parameters of Morrey-type spaces and the characteristics of the operator, which made it possible to expand the existing results previously known only in special cases. The conditions considered in the paper are not only sufficient, but also turn out to be necessary, which emphasizes their accuracy and optimality. The results obtained play an important role in the theory of integral-type operators and can also be applied in other areas of analysis, such as the theory of differential equations and theoretical physics. Thus, the study makes a significant contribution to the study of Riesz potential operators in Morrey-type spaces and opens up new prospects for future studies in this field. A similar result for the generalized truncated Riesz potential in L_p spaces was obtained in [10].

MATIN D.T.

PhD Doctor, Associate Professor, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan.

Е-mail: d.matin@mail.kz, https://orcid.org/0000-0002-9784-9304

AKHAZHANOV T.B.

PhD Doctor, Associate Professor, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan.

Е-mail: talgat_a2008@mail.ru, https://orcid.org/0000-0001-8539-1802

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