Geodesic
Singular integral characterization of nonisotropic generalized BMO spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 225-238 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We extend a result of Coifman and Dahlberg [{\it 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 $\Bbb R^n$ 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 $\Bbb R^n$ 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$_\varphi$ under a natural condition on $\varphi$.
We extend a result of Coifman and Dahlberg [{\it 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 $\Bbb R^n$ 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 $\Bbb R^n$ 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$_\varphi$ under a natural condition on $\varphi$.
Classification : 42B30, 42B99, 46E15
Keywords: singular integral; nonisotropic generalized BMO 
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     title = {Singular integral characterization of nonisotropic generalized {BMO} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {225--238},
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Crescimbeni, Raquel. Singular integral characterization of nonisotropic generalized BMO spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 225-238. http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a4/