Geodesic
Relation between the Gurov–Reshetnyak and the Muckenhoupt function classes
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 919-926 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the one-dimensional case, for a function satisfying the Gurov–Reshetnyak condition, the infimum of the indices of the Muckenhoupt classes containing this function is found. It is also shown that each Muckenhoupt class lies in some Gurov–Reshetnyak class. 
@article{SM_2003_194_6_a6,
     author = {A. A. Korenovskii},
     title = {Relation between {the~Gurov{\textendash}Reshetnyak} and {the~Muckenhoupt} function classes},
     journal = {Sbornik. Mathematics},
     pages = {919--926},
     year = {2003},
     volume = {194},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/}
}
TY  - JOUR
AU  - A. A. Korenovskii
TI  - Relation between the Gurov–Reshetnyak and the Muckenhoupt function classes
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 919
EP  - 926
VL  - 194
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/
LA  - en
ID  - SM_2003_194_6_a6
ER  - 
%0 Journal Article
%A A. A. Korenovskii
%T Relation between the Gurov–Reshetnyak and the Muckenhoupt function classes
%J Sbornik. Mathematics
%D 2003
%P 919-926
%V 194
%N 6
%U http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/
%G en
%F SM_2003_194_6_a6
A. A. Korenovskii. Relation between the Gurov–Reshetnyak and the Muckenhoupt function classes. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 919-926. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/

[1] Gurov L. G., “Ob ustoichivosti preobrazovanii Lorentsa. Otsenki dlya proizvodnykh”, Dokl. AN SSSR, 220:2 (1975), 273–276 | MR | Zbl

[2] Gurov L. G., Reshetnyak Yu. G., “Ob odnom analoge ponyatiya funktsii s ogranichennym srednim kolebaniem”, Sib. matem. zhurn., 17:3 (1976), 540–546 | MR | Zbl

[3] Iwaniec T., “On $L^p$-integrability in PDEs and quasiregular mappings for large exponents”, Ann. Acad. Sci. Fenn. Math., 7:2 (1982), 301–322 | MR | Zbl

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

[5] Wik I., “Note on a theorem by Reshetnyak–Gurov”, Studia Math., 86:3 (1987), 287–290 | MR | Zbl

[6] Franciosi M., “Weighted rearrangements and higher integrability results”, Studia Math., 92:2 (1989), 131–139 | MR | Zbl

[7] Franciosi M., “On weak reverse integral inequalities for mean oscillation”, Proc. Amer. Math. Soc., 113:1 (1991), 105–112 | DOI | MR | Zbl

[8] Korenovskii A. A., “One refinement of the Gurov–Reshetnyak inequality”, Ricerche Mat., 45:1 (1996), 197–204 | MR | Zbl

[9] Korenovskii A. A., “O svyazi mezhdu srednimi kolebaniyami i tochnymi pokazatelyami summiruemosti funktsii”, Matem. sb., 181:12 (1990), 1721–1727 | MR | Zbl

[10] Korenovskyy A. A., Lerner A. K., Stokolos A. M., A note on the Gurov–Reshetnyak condition, arXiv: math.CA/0205001

[11] Coifman R. R., Fefferman Ch., “Weighted norm inequalities for maximal functions and singular integrals”, Studia Math., 15 (1974), 241–250 | MR

[12] Strömberg J. O., Torchinsky A., Weighted Hardy spaces, Lecture Notes in Math., 1381, Springer-Verlag, Berlin, 1989 | MR | Zbl

[13] Klemes I., “A mean oscillation inequality”, Proc. Amer. Math. Soc., 93 (1985), 497–500 | DOI | MR | Zbl

[14] Garnett Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl