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Endpoint estimates and weighted norm inequalities for commutators of fractional integrals
Cruz-Uribe, D. (Trinity College. Department of Mathematics)
Fiorenza, A. (Universitá di Napoli. Dipartimento di Costruzioni e Metodi Matematici in Architettura)

Data: 2003
Resum: We prove that the commutator [b, Iα], b ∈ BMO, Iα the fractional integral operator, satisfies the sharp, modular weak-type inequality f(x) tdx, where B(t) = tlog(e + t) and Ψ(t)=[tlog(e + tα/n)]n/(n−α). These commutators were first considered by Chanillo, and our result complements his. The heart of our proof consists of the pointwise inequality, M#([b, Iα]f)(x) ≤ CbBMO [Iαf(x) + Mα,Bf(x)], where M# is the sharp maximal operator, and Mα,B is a generalization of the fractional maximal operator in the scale of Orlicz spaces. Using this inequality we also prove one-weight inequalities for the commutator; to do so we prove one and two-weight norm inequalities for Mα,B which are of interest in their own right. [b, Iα]f(x).
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Fractional integrals ; Commutators ; BMO ; Orlicz spaces ; Maximal functions ; Norm inequalities
Publicat a: Publicacions matematiques, V. 47 N. 1 (2003) , p. 103-131, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_47103_05
DOI: 10.5565/38068

29 p, 243.3 KB

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