# On continuity properties of functions with conditions on the mean oscillation

Studia Mathematica (1993)

- Volume: 106, Issue: 2, page 139-151
- ISSN: 0039-3223

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topAimar, Hugo, and Forzani, Liliana. "On continuity properties of functions with conditions on the mean oscillation." Studia Mathematica 106.2 (1993): 139-151. <http://eudml.org/doc/216009>.

@article{Aimar1993,

abstract = {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.},

author = {Aimar, Hugo, Forzani, Liliana},

journal = {Studia Mathematica},

keywords = {degenerate parabolic equations; BMO functions; type condition; distribution; continuity; vanishing mean oscillation; lag mapping; space of homogeneous type},

language = {eng},

number = {2},

pages = {139-151},

title = {On continuity properties of functions with conditions on the mean oscillation},

url = {http://eudml.org/doc/216009},

volume = {106},

year = {1993},

}

TY - JOUR

AU - Aimar, Hugo

AU - Forzani, Liliana

TI - On continuity properties of functions with conditions on the mean oscillation

JO - Studia Mathematica

PY - 1993

VL - 106

IS - 2

SP - 139

EP - 151

AB - 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.

LA - eng

KW - degenerate parabolic equations; BMO functions; type condition; distribution; continuity; vanishing mean oscillation; lag mapping; space of homogeneous type

UR - http://eudml.org/doc/216009

ER -

## References

top- [A1] H. Aimar, Rearrangement and continuity properties of BMO (ϕ) functions on spaces of homogeneous type, Ann. Scuola Norm. Sup. Pisa, to appear.
- [A2] H. Aimar, Elliptic and parabolic BMO and Harnack's inequality, Trans. Amer. Math. Soc. 306 (1988), 265-276. Zbl0675.42020
- [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. Zbl0368.46037
- [C] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188.
- [CS] F. Chiarenza and R. Serapioni, A Harnack inequality for degenerate parabolic equations, Comm. Partial Differential Equations 9 (1984), 719-749. Zbl0546.35035
- [CW] R. Coifman et R. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin 1972.
- [FG] E. Fabes and N. Garofalo, Parabolic BMO and Harnack's inequality, Proc. Amer. Math. Soc. 95 (1985), 63-69. Zbl0583.35051
- [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. Zbl0102.04302
- [Me] G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717-724. Zbl0129.04002
- [M1] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. Zbl0111.09302
- [M2] J. Moser, A Harnack inequality for parabolic differential equations, ibid. 17 (1964), 101-134; Correction, ibid. 20 (1967), 232-236.
- [MS] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. Zbl0431.46018
- [MT] F. Martín-Reyes and A. de la Torre, preprint.
- [N] U. Neri, Some properties of functions with bounded mean oscillation, Studia Math. 61 (1977), 63-75. Zbl0348.26013
- [S] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608. Zbl0199.44303

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