Publications
Article · Mathematics · January 17, 2024
Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces
Nurzhan Bokayev, Dauren Matin, Talgat Akhazhanov, A.N. Adilkhanov
Abstract
In this paper, we give the sufficient conditions for the compactness of sets in generalized Morrey spaces Mpw(·). This result is an analogue of the well-known Fréchet–Kolmogorov theorem on the compactness of a set in Lebesgue spaces Lp,p>0. As an application, we prove the compactness of the commutator of the Riesz potential [b,Iα] in generalized Morrey spaces, where b∈VMO (VMO(Rn) denote the BMO-closure of C0∞(Rn)). We prove auxiliary statements regarding the connection between the norm of average functions and the norm of the difference of functions in the generalized Morrey spaces. Such results are also of independent interest.
Advanced Harmonic Analysis ResearchMathematical Analysis and Transform MethodsAdvanced Banach Space Theorygeneralized Morrey spacesRiesz potentialcommutators
More by Nurzhan Bokayev
- Characterization of the boundedness of the discrete Fractional maximal operator between weighted in Lorentz sequence spacesarXiv · 2026
- Characterization of weighted inequalities for superpositions of integral and supremal operatorsBULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS · 2026
- Characterization of weighted inequalities for superpositions of integral and supremal operatorsBULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS · 2026
- Weighted Hardy inequalities involving supremum for decreasing sequencesZeitschrift für Analysis und ihre Anwendungen · 2026