L^p estimates for the maximal singular integral in terms of the\n singular integral

2013/02/22 by Anna Bosch-Camós, Bosch-Camós, Anna, Joan Mateu +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1302.5551

Abstract

This paper continues the study, initiated in the works MOV and MOPV, of\nthe problem of controlling the maximal singular integral T^*f by the\nsingular integral Tf. Here T is a smooth homogeneous Calder 'on-Zygmund\nsingular integral operator of convolution type. We consider two forms of\ncontrol, namely, in the weighted L^p(\ω) norm and via pointwise estimates\nof T^*f by M(Tf) or M²(Tf) ,, where M is the Hardy-Littlewood\nmaximal operator and M²=M \∘ M its iteration. The novelty with respect to\nthe aforementioned works, lies in the fact that here p is different from 2\nand the L^p space is weighted.\n

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