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Singular integral characterization of nonisotropic generalized BMO spaces

Raquel Crescimbeni — 2007

Commentationes Mathematicae Universitatis Carolinae

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 H p spaces by singular integrals of n with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if T λ is the family of dilations in n induced by a matrix with a nonnegative eigenvalue, then there exist 2 n singular integral operators homogeneous with respect to the dilations T λ that...

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