Abstract
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 Calderón-Zygmund singular integral operator of convolution type. We consider two forms of control, namely, in the weighted L p(ω) norm and via pointwise estimates of T* f by M(Tf ) or M 2(Tf), where M is the Hardy-Littlewood maximal operator and M 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 p space is weighted.
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The authors were partially supported by grants 2014SGR75 (Generalitat de Catalunya) and MTM2013-44699-P (Ministerio de Ciencia e Innovación, Spain).
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Bosch-Camós, A., Mateu, J. & Orobitg, J. L P estimates for the maximal singular integral in terms of the singular integral. JAMA 126, 287–306 (2015). https://doi.org/10.1007/s11854-015-0018-0
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DOI: https://doi.org/10.1007/s11854-015-0018-0