Geodesic
Hardy Inequality in Variable Grand Lebesgue Spaces for Nonincreasing Functions
Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 283-294.

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

In this paper, we study the boundedness of the Hardy averaging operator between weighted variable grand Lebesgue spaces for nonincreasing functions.
Mots-clés : variable Lebesgue space, variable grand Lebesgue space
Keywords: Hardy averaging operator, nonincreasing functions, weights. 
@article{MZM_2023_113_2_a10,
     author = {M. Singh and P. Jain},
     title = {Hardy {Inequality} in {Variable} {Grand} {Lebesgue} {Spaces} for {Nonincreasing} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {283--294},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a10/}
}
TY  - JOUR
AU  - M. Singh
AU  - P. Jain
TI  - Hardy Inequality in Variable Grand Lebesgue Spaces for Nonincreasing Functions
JO  - Matematičeskie zametki
PY  - 2023
SP  - 283
EP  - 294
VL  - 113
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a10/
LA  - ru
ID  - MZM_2023_113_2_a10
ER  - 
%0 Journal Article
%A M. Singh
%A P. Jain
%T Hardy Inequality in Variable Grand Lebesgue Spaces for Nonincreasing Functions
%J Matematičeskie zametki
%D 2023
%P 283-294
%V 113
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a10/
%G ru
%F MZM_2023_113_2_a10
M. Singh; P. Jain. Hardy Inequality in Variable Grand Lebesgue Spaces for Nonincreasing Functions. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 283-294. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a10/

[1] M. A. Arino, B. Muckenhoupt, “Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions”, Trans. Amer. Math. Soc., 320 (1990), 727–735 | MR

[2] C. J. Neugebauer, “Weighted norm inequalities for averaging operators of monotone functions”, Publ. Mat., 35 (1991), 429–447 | DOI | MR

[3] I. V. Tsenov, “Obobschenie zadachi o nailuchshem priblizhenii funktsii v prostranstve $\mathcal L^s$”, Uch. zap. Dagestanskogo un-ta, 7 (1961), 25–37

[4] O. Kováčik, J. Rákosník, “On $L^{p(x)}$ and $W^{k,p(x)}$ spaces”, Czech. Math. J., 41 (1991), 592–618 | DOI | MR

[5] I. I. Sharapudinov, “O topologii prostranstva $\mathscr L^{p(t)}([0,1])$”, Matem. zametki, 26:4 (1979), 613–632 | MR | Zbl

[6] D. V. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces. Foundations and Harmonic Analysis, Birkhäuser, Heidelberg, 2013 | MR

[7] C. J. Neugebauer, “Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions”, Studia Math., 192 (2009), 51–60 | DOI | MR

[8] A. Fiorenza, V. Kokilashvili, A. Meskhi, “Hardy–Littlewood maximal operator in weighted grand variable exponent Lebesgue space”, Mediterr. J. Math., 14 (2017), Paper No. 118 | DOI | MR

[9] L. Greco, T. Iwaniec, C. Sbordone, “Inverting the p-harmonic operator”, Manuscripta Math., 92 (1997), 249–258 | DOI | MR

[10] T. Iwaniec, C. Sbordone, “On the integrability of the Jacobian under minimal hypotheses”, Arch. Ration. Mech. Anal., 119 (1992), 129–143 | DOI | MR

[11] A. Fiorenza, B. Gupta, P. Jain, “The maximal theorem for weighted grand Lebesgue spaces”, Studia Math., 188 (2008), 123–133 | DOI | MR

[12] C. Capone, A. Fiorenza, “On small Lebesgue spaces”, J. Funct. Spaces Appl., 3 (2005), 73–89 | DOI | MR

[13] A. Fiorenza, “Duality and reflexivity in grand Lebesgue spaces”, Collect. Math., 51 (2000), 131–148 | MR

[14] A. Fiorenza, G. E. Karadzhov, “Grand and small Lebesgue spaces and their analogs”, Z. Anal. Anwendungen, 23 (2004), 657–681 | MR

[15] A. Fiorenza, J. M. Rakotoson, “New properties of small Lebesgue spaces and their applications”, Math. Ann., 326 (2003), 543–561 | DOI | MR

[16] P. Jain, S. Kumari, “On grand Lorentz spaces and the maximal operator”, Georgian Math. J., 19 (2012), 235–246 | DOI | MR

[17] P. Jain, M. Singh, A. P. Singh, “Hardy type operators on grand Lebesgue spaces for non-increasing functions”, Trans. A. Razmadze Math. Inst., 170 (2016), 34–46 | DOI | MR

[18] P. Jain, M. Singh, A. P. Singh, “Integral operators on fully measurable weighted grand Lebesgue spaces”, Indag. Math., 28 (2017), 516–526 | DOI | MR

[19] P. Jain, M. Singh, A. P. Singh, “Recent trends in grand Lebesgue spaces”, Function Spaces and Inequalities, Springer Proc. Math. Stat., 206, eds. P. Jain, H. J. Schmeisser, Springer, Singapore, 2017, 137–159 | MR

[20] V. M. Kokilashvili, “Kriterii ogranichennosti dlya singulyarnykh integralov v vesovykh grand-prostranstvakh Lebega”, Problemy matematicheskogo analiza, vyp. 49, TamaraRozhkovskaya, Novosibirsk, 2010, 19–30

[21] V. Kokilashvili, A. Meskhi, “Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces”, Georgian Math. J., 21 (2014), 447–461 | DOI | MR

[22] V. Kokilashvili, A. Meskhi, “Maximal and singular integral operators in weighted grand variable exponent Lebesgue spaces”, Ann. Funct. Anal., 12 (2021), 48 | DOI | MR

[23] A. N. Meskhi, “Vesovye kriterii dlya preobrazovaniya Khardi pri uslovii $B_p$ v grand-prostranstvakh Lebega i nekotorye prilozheniya”, Problemy matematicheskogo analiza, vyp. 60, Tamara Rozhkovskaya, Novosibirsk, 2011, 53–64

[24] M. Singh, “Grand and small $X^p$ spaces and generalized duality”, Positivity, 25 (2021), 1469–1488 | DOI | MR

[25] A. P. Singh, M. Singh, P. Jain, R. Panchal, “Rubio de Francia extrapolation theorem in variable Lebesgue spaces for $B_p(\,\cdot\,)$ weights”, Ricerche Mat., 2021 | DOI

[26] S. Boza, J. Soria, “Weighted Hardy modular inequalities in variable $L_p$ spaces for decreasing functions”, J. Math. Anal. Appl., 348 (2008), 383–388 | DOI | MR