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Zbl 0543.42013
Carton-Lebrun, C.; Fosset, M.
Moyennes et quotients de Taylor dans BMO.
(French)
[J] Bull. Soc. R. Sci. Liège 53, 85-87 (1984). ISSN 0037-9565/e

The main results of the paper are, that under certain conditions on $\psi$ the mean operator $P:f\to Pf$ with $(Pf)(x):=\int\sp{1}\sb{0}f(tx)\psi(t)dt$ is bounded from $BMO(R\sp n)$ into itself and, moreover, commutes with the Hilbert-transform (the case $n=1)$ and with certain Caldéron-Zygmund operators (and thus with the Riesz-operator) in the case $n\ge 2$.
[M.G.de Bruin]
MSC 2000:
*42B20 Singular integrals, several variables
46E35 Sobolev spaces and generalizations
44A05 General integral transforms

Keywords: mean operator; $BMO(R\sp n)$; Hilbert-transform; Caldéron-Zygmund operators

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