Geodesic
The Function $G_\lambda^*$ as the Norm of a Calder\'on--Zygmund Operator
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 421-428.

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We describe a new approach to one of the quadratic functions in the Littlewood–Paley theory, namely, to the function $G_\lambda^*$. It is shown that some of its properties can be obtained from the general theory of operators of Calderón–Zygmund type (which, apparently, has not been considered applicable in this context). There are applications to interpolation theory.
Keywords: Calderón–Zygmund operator, Hilbert space, Brownian motion, Banach space, Hardy class $H^p$, Cauchy's inequality.
Mots-clés : Poisson kernel, Lebesgue measure 
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N. N. Osipov. The Function $G_\lambda^*$ as the Norm of a Calder\'on--Zygmund Operator. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 421-428. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a11/

[1] I. M. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[2] C. Fefferman, “Inequalities for strongly singular convolution operators”, Acta Math., 124 (1970), 9–36 | MR | Zbl

[3] P. W. Jones, P. F. X. Müller, “Conditioned Brownian motion and multipliers into $SL^\infty$”, Geom. Funct. Anal., 14:2 (2004), 319–379 | MR | Zbl

[4] D. S. Anisimov, S. V. Kislyakov, “Dvoinye singulyarnye integraly: interpolyatsiya i ispravlenie”, Algebra i analiz, 16:5 (2004), 1–33 | MR | Zbl

[5] S. V. Kisliakov, “Interpolation of $H^p$-spaces: some recent developments”, Function spaces, interpolation spaces, and related topics (Haifa, 1995), Israel Math. Conf. Proc., 13, Bar-Ilan Univ., Ramat Gan, 1999, 102–140 | MR | Zbl