Geodesic
On the Reverse H\"older Inequality
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 361-373.

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

We obtain exact positive and negative exponents of integrability of a function satisfying the reverse weighted Hölder inequality on parallelepipeds.
Keywords: reverse Hölder inequality, Gehring's function class, Muckenhoupt's function class, Hardy's inequality, exponent of integrability. 
@article{MZM_2007_81_3_a5,
     author = {A. A. Korenovskii},
     title = {On the {Reverse} {H\"older} {Inequality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--373},
     publisher = {mathdoc},
     volume = {81},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a5/}
}
TY  - JOUR
AU  - A. A. Korenovskii
TI  - On the Reverse H\"older Inequality
JO  - Matematičeskie zametki
PY  - 2007
SP  - 361
EP  - 373
VL  - 81
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a5/
LA  - ru
ID  - MZM_2007_81_3_a5
ER  - 
%0 Journal Article
%A A. A. Korenovskii
%T On the Reverse H\"older Inequality
%J Matematičeskie zametki
%D 2007
%P 361-373
%V 81
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a5/
%G ru
%F MZM_2007_81_3_a5
A. A. Korenovskii. On the Reverse H\"older Inequality. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 361-373. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a5/

[1] B. Muckenhoupt, “Wieghted norm inequalities for the Hardy maximal function”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[2] F. W. Gehring, “The $L^p$-integrability of the partial derivatives of a quasiconformal mapping”, Acta Math., 130 (1973), 265–277 | DOI | MR | Zbl

[3] R. R. Coifman, Ch. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals”, Studia Math., 51 (1974), 241–250 | MR | Zbl

[4] B. Bojarski, “Remarks on the stability of reverse Hölder inequalities and quasiconformal mappings”, Ann. Acad. Sci. Fenn. Ser. A. I. Math., 10 (1985), 89–94 | MR | Zbl

[5] B. Bojarski, On Gurov–Reshetnyak classes, Publ. Sci., Univ. Joensuu, 14, Univ. of Warsaw, 1989 | Zbl

[6] I. Wik, “Reverse Hölder inequalities with constant close to 1”, Ric. Math., 39:1 (1990), 151–157 | MR | Zbl

[7] L. D'Apuzzo, C. Sbordone, “Reverse Hölder inequalities. A sharp result”, Rend. Math. Appl. (7), 10:2 (1990), 357–366 | MR | Zbl

[8] A. A. Korenovskii, “O tochnom prodolzhenii obratnogo neravenstva Gëldera i usloviya Makenkhaupta”, Matem. zametki, 52:6 (1992), 32–44 | MR | Zbl

[9] A. Popoli, “Optimal integrability in $B^q_p$ classes”, Matematiche, 52:1 (1997), 159–170 | MR | Zbl

[10] A. Popoli, “Weighted reverse Hölder inequalities”, Rend. Accad. Sci. Fis. Mat. Napoli (4), 62 (1995), 187–211 | MR

[11] N. A. Malaksiano, “O tochnykh vlozheniyakh klassov Geringa v klassy Makenkhaupta”, Matem. zametki, 70:5 (2001), 742–750 | MR | Zbl

[12] N. Malaksiano, “The precise embeddings of the one-dimensional Muckenhoupt classes in Gehring classes”, Acta Sci. Math. (Szeged), 68:1–2 (2002), 237–248 | MR | Zbl

[13] V. I. Vasyunin, “Tochnaya konstanta v obratnom neravenstve Gëldera dlya makenkhauptovskikh vesov”, Algebra i analiz, 15:1 (2003), 73–117 | MR | Zbl

[14] J. Kinnunen, Sharp result on reverse Hölder inequalities, Ann. Acad. Sci. Fenn. Ser. A I. Math. Diss., 95, Suomalainen Tiedeakatemia, Helsinki, 1994 | MR | Zbl

[15] G. G. Khardi, D. E. Littlvud, G. Polia, Neravenstva, IL, M., 1948 | MR | Zbl

[16] G. H. Hardy, G. E. Littlewood, G. Polya, “Some simple inequalities satisfied by convex functions”, Messenger, 58 (1929), 145–152 | Zbl

[17] A. A. Korenovskii, “Otsenka perestanovki funktsii, udovletvoryayuschei “obratnomu neravenstvu Iensena””, Ukr. matem. zhurn., 57:2 (2005), 158–169 | MR | Zbl