Geodesic
Hardy-type inequality for $0$ and hypodecreasing functions
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 27-42 
V. I. Burenkov; A. Senouci; T. V. Tararykova. Hardy-type inequality for $0
@article{EMJ_2010_1_3_a2,
     author = {V. I. Burenkov and A. Senouci and T. V. Tararykova},
     title = {Hardy-type inequality for $0<p<1$ and hypodecreasing functions},
     journal = {Eurasian mathematical journal},
     pages = {27--42},
     year = {2010},
     volume = {1},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a2/}
}
TY  - JOUR
AU  - V. I. Burenkov
AU  - A. Senouci
AU  - T. V. Tararykova
TI  - Hardy-type inequality for $0
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 27
EP  - 42
VL  - 1
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a2/
LA  - en
ID  - EMJ_2010_1_3_a2
ER  - 
%0 Journal Article
%A V. I. Burenkov
%A A. Senouci
%A T. V. Tararykova
%T Hardy-type inequality for $0
%J Eurasian mathematical journal
%D 2010
%P 27-42
%V 1
%N 3
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a2/
%G en
%F EMJ_2010_1_3_a2

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

The notion of a hypodecreasing function is introduced. Some properties of hypodecreasing functions are proved and several examples are given. It is established that the Hardy-type inequality for $L_p$-spaces with $0$ is satisfied for some spaces of hypodecreasing functions. The obtained result is in a certain sense sharp.

[1] J. Bergh, V. Burenkov, L.-E. Persson, “Best constants in reversed Hardy's inequalities for quasi monotone functions”, Acta Sci. Math. (Szeged), 59:1–2 (1994), 221–239 | MR | Zbl

[2] J. Bergh, V. Burenkov, L.-E. Persson, “On some sharp reversed Hölder and Hardy-type inequalities”, Math. Nachr., 169 (1994), 19–29 | DOI | MR | Zbl

[3] V. I. Burenkov, Function spaces. Main integral inequalities related to $L_p$-spaces, Peoples' Friendship University, Moscow, 1989 (in Russian)

[4] Proc. Steklov Inst. Math., 194:4 (1993), 59–63 | MR | Zbl

[5] V. I. Burenkov, Sobolev spaces on domains, B. G. Teubner, Stuttgart, Leipzig, 1997 | MR

[6] V. I. Burenkov, A. Senouci, T. V. Tararykova, “Equivalent quasi-norm involving differences and moduli of continuity”, Complex Variables and Elliptic Equations, 55:8–10 (2010), 759–769 | DOI | MR | Zbl

[7] A. Senouci, T. V. Tararykova, “Hardy-type inequality for $0

1$”, Evraziiskii Matematicheskii Zhurnal, 2 (2007), 112–116