Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces
Bokayev N. Burenkov V. Matin D. Adilkhanov A.
November 2024Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2024#12Issue 22
In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces (Formula presented.). Our main result is the compactness of the commutators of the Riesz potential (Formula presented.) in global Morrey-type spaces from (Formula presented.) to (Formula presented.). We also present new sufficient conditions for the commutator (Formula presented.) to be bounded from (Formula presented.) to (Formula presented.). In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential (Formula presented.) in global Morrey-type spaces (Formula presented.), and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces (Formula presented.).
commutator , compactness , global Morrey space , Riesz potential , VMO
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Faculty of Mechanics and Mathematics, L.N. Gumilyov, Eurasian National University, Astana, 010000, Kazakhstan
V.A. Steklov Mathematical Institute, Russian Academy of Sciences, 42 Gubkin St, Moscow, 117966, Russian Federation
V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya St, Moscow, 117997, Russian Federation
Faculty of Mechanics and Mathematics
V.A. Steklov Mathematical Institute
V.A. Trapeznikov Institute of Control Sciences
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