Work

Compactness of Commutators for Riesz Potential on Generalized Morrey Spaces

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12020304

Authors: Nurzhan Bokayev, Dauren Matin, Talgat Akhazhanov, Aidos Adilkhanov

Institution: L. N. Gumilyov Eurasian National University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: Ministry of Science and Higher Education of the Republic of Kazakhstan