Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
Компактность коммутаторов для потенциала Рисса в локальных пространствах типа Морри
Локальдi Морри типтес кеңiстiгiнде Рисс потенциал коммутаторының компактылығы
Matin D.T. Akhazhanov T.B. Adilkhanov A.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 293 - 103 pp.
The paper considers Morrey-type local spaces from LMpθw The main work is the proof of the commutator compactness theorem for the Riesz potential [b,Iα] in local Morrey-type spaces from LMpθw1 to LMqθw2. We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b,Iα] in local Morrey-type spaces from LMpθw1 to LMqθw2. In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b,Iα] in local Morrey-type spaces LMpθw, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LMpθw. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b,Iα]. Similar results were obtained for global Morrey-type spaces GMpθw and for generalized Morrey spaces Mpw
Commutators , Compactness , Local Morrey-type spaces , Riesz Potential
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
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