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Eurasian Mathematical Journal, 2023, Volume 14, Number 2, Pages 13–23
DOI: https://doi.org/10.32523/2077-9879-2023-14-2-13-23 (Mi emj467) 		 
On estimates of non-increasing rearrangement of generalized fractional maximal function

N. A. Bokayeva, A. Gogatishvilib, A. N. Abeka

a Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Munaitpasov St., 010008 Astana, Kazakhstan
b Institute of Mathematics of the Czech Academy of Sciences, 25 Zitna St., Prague, CZ- 115 67, Czech Republic
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DOI: https://doi.org/10.32523/2077-9879-2023-14-2-13-23
Abstract: We give a sharp pointwise estimate of the non-increasing rearrangement of the generalized fractional maximal function $(M_\Phi f)(x)$ via an expression involving the non-increasing rearrangement of $f$. It is shown that the obtained estimate is more sharp than the inequality which follows from the estimate for the generalized Riesz potential.
Keywords and phrases: generalized fractional maximal function, non-increasing rearrangements, generalized Riesz potential.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP14869887
Czech Science Foundation (GACR) RVO: 67985840
Shota Rustaveli National Science Foundation FR21-12353
The research of N.A. Bokayev, A. Gogatishvili, A.N. Abek was supported by the grant Ministry of Science and Higher Education of the Republic of Kazakhstan (project no. AP14869887). The research of A. Gogatishvili was supported by Czech Academy of Sciences RVO: 67985840 and by Shota Rustaveli National Science Foundation (SRNSF), grant no. FR21-12353.
Received: 06.06.2022
Document Type: Article
MSC: 42B25, 46E30, 47B38
Language: English
Citation: N. A. Bokayev, A. Gogatishvili, A. N. Abek, “On estimates of non-increasing rearrangement of generalized fractional maximal function”, Eurasian Math. J., 14:2 (2023), 13–23
Citation in format AMSBIB
\Bibitem{BokGogAbe23}
\by N.~A.~Bokayev, A.~Gogatishvili, A.~N.~Abek
\paper On estimates of non-increasing rearrangement of generalized fractional maximal function
\jour Eurasian Math. J.
\yr 2023
\vol 14
\issue 2
\pages 13--23
\mathnet{http://mi.mathnet.ru/emj467}
\crossref{https://doi.org/10.32523/2077-9879-2023-14-2-13-23}
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