Bloom weighted bounds for sparse forms associated to commutators

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review


In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner–Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón–Zygmund operators, the previously known quantitative Bloom bounds are not sharp for the second and higher order commutators.

Original languageEnglish
Article number73
JournalMathematische Zeitschrift
Issue number4
StatePublished - Apr 2024


  • 42B20
  • 42B25
  • 47B47
  • Bilinear sparse forms
  • Bloom weighted bounds
  • Iterated commutators

All Science Journal Classification (ASJC) codes

  • General Mathematics


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