On continuity properties of functions with conditions on the mean oscillation
Aimar, Hugo ; Forzani, Liliana
Studia Mathematica, Tome 104 (1993), p. 139-151 / Harvested from The Polish Digital Mathematics Library
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In this paper we study distribution and continuity properties of functions satisfying a vanishing mean oscillation property with a lag mapping on a space of homogeneous type.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:216009 
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     title = {On continuity properties of functions with conditions on the mean oscillation},
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     volume = {104},
     year = {1993},
     pages = {139-151},
     zbl = {0821.42014},
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Aimar, Hugo; Forzani, Liliana. On continuity properties of functions with conditions on the mean oscillation. Studia Mathematica, Tome 104 (1993) pp. 139-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i2p139bwm/

[00000] [A1] H. Aimar, Rearrangement and continuity properties of BMO (ϕ) functions on spaces of homogeneous type, Ann. Scuola Norm. Sup. Pisa, to appear.

[00001] [A2] H. Aimar, Elliptic and parabolic BMO and Harnack's inequality, Trans. Amer. Math. Soc. 306 (1988), 265-276. | Zbl 0675.42020

[00002] [B] N. Burger, Espace des fonctions à moyenne bornée sur un espace de nature homogène, C. R. Acad. Sci. Paris Sér. A 286 (1978), 139-142. | Zbl 0368.46037

[00003] [C] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188.

[00004] [CS] F. Chiarenza and R. Serapioni, A Harnack inequality for degenerate parabolic equations, Comm. Partial Differential Equations 9 (1984), 719-749. | Zbl 0546.35035

[00005] [CW] R. Coifman et R. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin 1972.

[00006] [FG] E. Fabes and N. Garofalo, Parabolic BMO and Harnack's inequality, Proc. Amer. Math. Soc. 95 (1985), 63-69. | Zbl 0583.35051

[00007] [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. | Zbl 0102.04302

[00008] [Me] G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717-724. | Zbl 0129.04002

[00009] [M1] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. | Zbl 0111.09302

[00010] [M2] J. Moser, A Harnack inequality for parabolic differential equations, ibid. 17 (1964), 101-134; Correction, ibid. 20 (1967), 232-236.

[00011] [MS] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. | Zbl 0431.46018

[00012] [MT] F. Martín-Reyes and A. de la Torre, preprint.

[00013] [N] U. Neri, Some properties of functions with bounded mean oscillation, Studia Math. 61 (1977), 63-75. | Zbl 0348.26013

[00014] [S] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608. | Zbl 0199.44303