Singular integral characterization of nonisotropic generalized BMO spaces

We extend a result of Coffman and Dahlberg [Singular integral characterizations of nonisotropic H-P spaces and the F. and M. Riesz theorem, Proc. Sympos. Pure Math., Vol. 35, pp. 231-234; Amer. Math. Soc., Providence, 1979] on the characterization of H-P spaces by singular integrals of R-n with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if T-lambda is the family of dilations in R-n induced by a matrix with a nonnegative eigenvalue, then there exist 2n singular integral operators homogeneous with respect to the dilations T-lambda that characterize BMO phi under a natural condition on phi.