Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 13-26

BMO ON SPACES OF HOMOGENEOUS TYPE: A DENSITY RESULT ON C-C SPACES

A.O. Caruso and M.S. Fanciullo

Dipartimento di Matematica e Informatica, Università di Catania
Viale A. Doria 6 - I, 95125, Catania, Italy; aocaruso 'at' dmi.unict.it

Dipartimento di Matematica e Informatica, Università di Catania
Viale A. Doria 6 - I, 95125, Catania, Italy; fanciullo 'at' dmi.unict.it

Abstract. In the general setting of a space of homogeneous type endowed with an Ahlfors regular measure, we introduce the Banach spaces BMO and VMO defined through suitable cubes, and we prove that these spaces are topologically equivalent to the standard ones usually defined by means of balls. Through this fact we extend a known result of Sarason showing that C^\infty is locally dense in VMO in the setting of Carnot-Carathéodory metric spaces related to a family of free Hörmander vector fields X₁,...,X_q.

2000 Mathematics Subject Classification: Primary 43A80, 46E30, 46E35, 54E35.

Key words: VMO, spaces of homogeneous type, Carnot-Carathéodory metric, Ahlfors regular measures.

Reference to this article: A.O. Caruso and M.S. Fanciullo: BMO on spaces of homogeneous type: A density result on C-C spaces. Ann. Acad. Sci. Fenn. Math. 32 (2007), 13-26.

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