On the connection between mean oscillation and exact integrability classes of functions
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 561-567 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exact integrability classes are obtained for the functions in the John–Nirenberg and Gurov–Reshetnyak inequalities.
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A. A. Korenovskii. On the connection between mean oscillation and exact integrability classes of functions. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 561-567. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a18/

[1] John F., Nirenberg L., “On functions of bounded mean oscillation”, Comm. Pure Appl. Math., 14:4 (1961), 415–426 | DOI | MR | Zbl

[2] Gatnett J. B., Jones P. W., “The distance in BMO to $L^\infty$”, Ann. Math., 108 (1978), 373–393 | DOI | MR

[3] Bennett C., Sharpley R., “Weak type inequalities for $H^p$ and BMO”, Proc. Symp. Pure Math., 35:1 (1979), 201–229 | MR | Zbl

[4] Wik I., “On John and Nirenberg's theorem”, Dep. Math. Univ. Umea, 1985, no. 1, 1–12 (to appear)

[5] 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

[6] Bojarski B., “Remarks on the stability of inverse Hölder inequalities and quasiconformal mappings”, Ann. Acad. Sci. Fenn. Ser. A1, 1985, no. 10, 89–94 | MR | Zbl

[7] Franciosi M., Moscariello G., “Higher integrability results”, Manuscripta Math., 52:1–3 (1985), 151–170 | DOI | MR | Zbl

[8] Iwaniec T., “On $L^p$-integrability in PDE's and quasiregular mappings for large exponents”, Ann. Acad. Sci. Fenn. Ser. A1, 7 (1982), 301–322 | MR | Zbl

[9] Wik I., “Note on a theorem by Reśetnjak-Gurov”, Dep. Math. Univ. Umea, 1985, no. 6, 1–7 (to appear)

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

[11] Garsia A. M., Rodemich E., “Monotonicity of certain functionals under rearrangement”, Ann. Inst. Fourier, Grenoble, 24:2 (1974), 67–116 | MR | Zbl

[12] Bennett C., De Vore R. A., Sharpley R., “Weak-$L^\infty$ and BMO”, Ann. Math., 113:2 (1981), 601–611 | DOI | MR | Zbl

[13] Klemes I., “A mean oscillation inequality”, Proc. Amer. Math. Soc., 93:3 (1985), 497–500 | DOI | MR | Zbl