The factorization of H^p on the space of homogeneous type

Akihito Uchiyama

Vol. 92 (1981), No. 2, 453–468

DOI: 10.2140/pjm.1981.92.453

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,Ω≢0,
	Ω(rx) = Ω(x) when r > 0 and x ∈ Rn ∖{0},
	|Ω(x) − Ω(y)|≤|x − y| when |x| = |y| = 1,	(*)

and that

Let

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