On continuity properties of functions with conditions on the mean oscillation

Hugo Aimar; Liliana Forzani

Studia Mathematica (1993)

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

Abstract

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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.

How to cite

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Aimar, 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

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  1. [A1] H. Aimar, Rearrangement and continuity properties of BMO (ϕ) functions on spaces of homogeneous type, Ann. Scuola Norm. Sup. Pisa, to appear. 
  2. [A2] H. Aimar, Elliptic and parabolic BMO and Harnack's inequality, Trans. Amer. Math. Soc. 306 (1988), 265-276. Zbl0675.42020
  3. [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
  4. [C] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188. 
  5. [CS] F. Chiarenza and R. Serapioni, A Harnack inequality for degenerate parabolic equations, Comm. Partial Differential Equations 9 (1984), 719-749. Zbl0546.35035
  6. [CW] R. Coifman et R. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin 1972. 
  7. [FG] E. Fabes and N. Garofalo, Parabolic BMO and Harnack's inequality, Proc. Amer. Math. Soc. 95 (1985), 63-69. Zbl0583.35051
  8. [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. Zbl0102.04302
  9. [Me] G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717-724. Zbl0129.04002
  10. [M1] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. Zbl0111.09302
  11. [M2] J. Moser, A Harnack inequality for parabolic differential equations, ibid. 17 (1964), 101-134; Correction, ibid. 20 (1967), 232-236. 
  12. [MS] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. Zbl0431.46018
  13. [MT] F. Martín-Reyes and A. de la Torre, preprint. 
  14. [N] U. Neri, Some properties of functions with bounded mean oscillation, Studia Math. 61 (1977), 63-75. Zbl0348.26013
  15. [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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