On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture

Andrei K. Lerner, Fedor Nazarov, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We construct an example showing that the upper bound [w]A1 log(e+[w]A1) for the L1(w) → L1,∞(w) norm of the Hilbert transform cannot be improved in general.

Original languageEnglish
Pages (from-to)1939-1954
Number of pages16
JournalAnalysis and PDE
Issue number6
StatePublished - 2020

Bibliographical note

Funding Information:
Lerner is supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927, Nazarov is supported by U.S. National Science Foundation grant DMS-1600239, Ombrosi is supported by CONICET PIP 11220130100329CO, Argentina. MSC2010: 42B20, 42B25. Keywords: Hilbert transform, maximal operator, weighted inequalities.

Publisher Copyright:
© 2020 Mathematical Sciences Publishers.


  • Hilbert transform
  • Maximal operator
  • Weighted inequalities


Dive into the research topics of 'On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture'. Together they form a unique fingerprint.

Cite this