ON ESTIMATES OF NON-INCREASING REARRANGEMENT OF GENERALIZED FRACTIONAL MAXIMAL FUNCTION

Bokayev N.A. Gogatishvili A. Abek A.N.
2023 L.N. Gumilyov Eurasian National University

Eurasian Mathematical Journal
2023 #14 Issue 2 13 - 23 pp.

We give a sharp pointwise estimate of the non-increasing rearrangement of the generalized fractional maximal function (M_Φf)(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.

generalized fractional maximal function , generalized Riesz potential , non-increasing rearrangements

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Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Munaitpasov St., Astana, 010008, Kazakhstan
Institute of Mathematics of the Czech Academy of Sciences, 25 Zitna St., Prague, CZ-115 67, Czech Republic

Department of Mechanics and Mathematics
Institute of Mathematics of the Czech Academy of Sciences

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