Geodesic
On estimates of non-increasing rearrangement of generalized fractional maximal function
Eurasian mathematical journal, Tome 14 (2023) no. 2, pp. 13-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{EMJ_2023_14_2_a1,
     author = {N. A. Bokayev and A. Gogatishvili and A. N. Abek},
     title = {On estimates of non-increasing rearrangement of generalized fractional maximal function},
     journal = {Eurasian mathematical journal},
     pages = {13--23},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a1/}
}
TY  - JOUR
AU  - N. A. Bokayev
AU  - A. Gogatishvili
AU  - A. N. Abek
TI  - On estimates of non-increasing rearrangement of generalized fractional maximal function
JO  - Eurasian mathematical journal
PY  - 2023
SP  - 13
EP  - 23
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a1/
LA  - en
ID  - EMJ_2023_14_2_a1
ER  - 
%0 Journal Article
%A N. A. Bokayev
%A A. Gogatishvili
%A A. N. Abek
%T On estimates of non-increasing rearrangement of generalized fractional maximal function
%J Eurasian mathematical journal
%D 2023
%P 13-23
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a1/
%G en
%F EMJ_2023_14_2_a1
N. A. Bokayev; A. Gogatishvili; A. N. Abek. On estimates of non-increasing rearrangement of generalized fractional maximal function. Eurasian mathematical journal, Tome 14 (2023) no. 2, pp. 13-23. http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a1/

[1] N. K. Bari, S. B. Stechkin, “Best approximations and differential properties of two conjugate functions”, Tr. Mosk. Mat. Obs., 5, 1956, 483–522 (in Russian) | MR | Zbl

[2] C. Bennett, R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, 129, Academic Press, Boston, MA, 1988 | MR | Zbl

[3] N. A. Bokayev, M. L. Goldman, G. Zh. Karshygina, “Cones of functions with monotonicity conditions for generalized Bessel and Riesz potetials”, Mathem. Notes, 104:3 (2018), 356–373 | MR | Zbl

[4] N. A. Bokayev, M. L. Goldman, G. Zh. Karshygina, “Criteria for embeddings of generalized Bessel and Riesz poten tial spaces in rearrangement invariant spaces”, Eurasian Math. J., 10:2 (2019), 8–29 | DOI | MR | Zbl

[5] A. Cianchi, R. Kerman, B. Opic, L. Pick, “A sharp rearrangement inequality for the fractional maximal operator”, Studia Mathematica, 138:3 (2000), 277–284 | MR | Zbl

[6] A. Gogatishvili, L. Pick, B. Opic, “Weighted inequalities for Hardy-type operators involving suprema”, Collect. Math., 57:3 (2006), 227–255 | MR | Zbl

[7] M. L. Goldman, “Rearrangement invariant envelopes of generalized Bessel and Riesz potentials”, Reports of RAS, 423:1 (2008), 151–155 | MR

[8] M. L. Goldman, “On optimal embeddings of Bessel and Riesz potentials”, Proc. of the Steklov Inst. Math., 269 (2010), 91–111 | DOI | MR | Zbl

[9] M. L. Goldman, “On the cones of rearrangements for generalized Bessel and Riesz potentials”, Complex Variables and Elliptic Equations, 55:8-10 (2010), 817–832 | DOI | MR | Zbl

[10] M. L. Goldman, E. G. Bakhtigareeva, “Some classes of operators in general Morrey-type spaces”, Eurasian Math. J., 11:4 (2020), 35–44 | DOI | MR | Zbl

[11] D. I. Hakim, E. Nakai, Y. Sawano, “Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz-Morrey spaces”, Revista Matematica Complutense, 29 (2016), 59–90 | DOI | MR | Zbl

[12] A. Kucukaslan, “Equivalence of norms of the generalized fractional integral operator and the generalized fractional maximal operator on the generalized weighted Morrey spaces”, Annals of Functional Analysis, 11 (2020), 1007–1026 | DOI | MR | Zbl

[13] R. Ch. Mustafayev, N. Bilgicli, “Generalized fractional maximal functions in Lorentz spaces”, Journal of Mathematical Inequalities, 12:3 (2018), 827–851 | DOI | MR | Zbl

[14] R. O'Neil, “Convolution operators and $L(p,q)$ spaces”, Duke Math. J., 30 (1963), 129–142 | MR | Zbl