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A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition
Tolsa Domènech, Xavier (Université de Paris-Sud. Département de Mathématique)

Data: 2001
Resum: Given a doubling measure µ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(µ) are also of weak type (1, 1). Recently it has been shown that the same result holds if one substitutes the doubling condition on µ by a mild growth condition on µ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted to the non doubling situation.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 45 N. 1 (2001) , p. 163-174, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_45101_07

12 p, 147.7 KB

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