Annales AcademiŠ Scientiarum FennicŠ
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, UniversitÓ di Catania
Viale A. Doria 6 - I, 95125, Catania, Italy; aocaruso 'at' dmi.unict.it

Dipartimento di Matematica e Informatica, UniversitÓ 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-CarathÚodory metric spaces related to a family of free H÷rmander vector fields X1,...,Xq.

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

Key words: VMO, spaces of homogeneous type, Carnot-CarathÚodory 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.

Full document as PDF file

Copyright © 2007 by Academia Scientiarum Fennica