The maximal singular integral: Estimates in terms of the singular integral

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© Springer-Verlag Italia 2013. This paper considers estimates of the maximal singular integral T ⋆ f in terms of the singular integral Tf only. The most basic instance of the estimates we look for is the L 2 (ℝ n ) inequality ║T ⋆ f ║ 2 ≤ C║Tf║ 2 . We present the complete characterization, recently obtained by Mateu, Orobitg, Pérez and the author, of the smooth homogeneous convolution Calderón–Zygmund operators for which such inequality holds. We focus attention on special cases of the general statement to convey the main ideas of the proofs in a transparent way, as free as possible of the technical complications inherent to the general case. Particular attention is devoted to higher Riesz transforms.
Original languageEnglish
Pages (from-to)425-447
JournalSpringer INdAM Series
Publication statusPublished - 1 Jan 2017


  • Calderón–Zygmund operators
  • Fourier multipliers
  • Maximal singular integrals


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