On continuity properties of functions with conditions on the mean oscillation

• Autorzy: Hugo Aimar , Liliana Forzani
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 106
• Numer: 2
• Strony: 139-151

Daty

wydano

1993

otrzymano

1992-04-09

poprawiono

1992-12-07

Twórcy

autor

Hugo Aimar

• Programa Especial de Matemática Aplicada, Intec-Conicet, cc N° 91, 3000 Santa Fe, Argentina.

autor

Liliana Forzani

• Departamento de Matemática, Facultad de Ingeniería Química, UNL, Santiago del Estero 2829, 3000 Santa Fe, Argentina.

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
• [Me] G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717-724.
• [M1] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591.
• [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.
• [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.
• [S] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608.