Singular integral characterization of nonisotropic generalized BMO spaces
We extend a result of Coifman and Dahlberg [, Proc. Sympos. Pure Math., Vol. 35, pp. 231–234; Amer. Math. Soc., Providence, 1979] on the characterization of spaces by singular integrals of with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if is the family of dilations in induced by a matrix with a nonnegative eigenvalue, then there exist singular integral operators homogeneous with respect to the dilations that...