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Raquel Crescimbeni 5ECK=H EJACH= ?D=H=?JAHE=JE B EIJHFE? CAAH=EA@ * IF=?AI

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Raquel Crescimbeni

Singular integral characterization of nonisotropic generalized BMO spaces

Comment.Math.Univ.Carolin. 48,2 (2007) 225-238.

Abstract: We extend a result of Coifman and Dahlberg [Singular integral char- acterizations of nonisotropic Hp 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 ofHpspaces by singular integrals ofRnwith a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. More precisely, if Tλ is the family of dilations inRn induced by a matrix with a nonnegative eigenvalue, then there exist 2nsingular integral operators homo- geneous with respect to the dilations Tλ that characterize BMOϕ under a natural condition onϕ.

Keywords: singular integral, nonisotropic generalized BMO AMS Subject Classification: Primary 42B30; secondary 42B99

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