Vol. 92, No. 2, 1981

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The factorization of Hp on the space of homogeneous type

Akihito Uchiyama

Vol. 92 (1981), No. 2, 453–468
Abstract

Let K be a Calderon-Zygmund singular integral operator with smooth kernel. That is, there is an Ω(x) defined on Rn ∖{0} which satisfies

|x|=1 Ω = 0,Ω0,
Ω(rx) = Ω(x) when r > 0 and x Rn ∖{0},
|Ω(x) Ω(y)|≤|x y| when |x| = |y| = 1, (*)
and that
            ∫
Kf (x) = P.V.  Ω (x− y)|x − y|−nf (y)dy.
Rn

Let

            ∫
K ′f (x) = P.V.    Ω(y− x)|y− x|− nf(y)dy.
Rn

R. Coifman, R. Rochberg and G. Weiss showed the weak version of the factorization theorem of H1(Rn) and that was refined by Uchiyama in the following form.

Mathematical Subject Classification 2000
Primary: 42B30
Milestones
Received: 1 October 1979
Published: 1 February 1981
Authors
Akihito Uchiyama