L super( )Pestimates for the maximal singular integral in terms of the singular integral

This paper continues the study, initiated in [MOV] and [MOPV], of the problem of controlling the maximal singular integral T* f by the singular integral Tf. Here, T is a smooth homogeneous Calderon-Zygmund singular integral operator of convolution type. We consider two forms of control, namely, in t...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2015-04, Vol.126 (1), p.287-306
Main Authors: Bosch-Camos, Anna, Mateu, Joan, Orobitg, Joan
Format: Article
Language:English
Subjects:
Consumer goods
Convolution
Estimates
Integrals
Iterative methods
Norms
Operators
Online Access:Get full text
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Summary:This paper continues the study, initiated in [MOV] and [MOPV], of the problem of controlling the maximal singular integral T* f by the singular integral Tf. Here, T is a smooth homogeneous Calderon-Zygmund singular integral operator of convolution type. We consider two forms of control, namely, in the weighted L super( )p omega ) norm and via pointwise estimates of T* f by M(Tf ) or M super(2)(Tf), where M is the Hardy-Littlewood maximal operator and M super(2) = M po M its iteration. The novelty with respect to the aforementioned works lies in the fact that here p is different from 2 and the L super( )pspace is weighted.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-015-0018-0