Sharp A 2 inequality for Haar shift operators

Michael T. Lacey, Stefanie Petermichl, Maria Carmen Reguera

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


As a corollary to our main theorem we give a new proof of the result that the norm of the Hilbert transform on L^2(w) has norm bounded by a the A_2 characteristic of a weight to the first power, a theorem of one of us. This new proof begins as the prior proofs do, by passing to Haar shifts. Then, we apply a deep two-weight T1 theorem of Nazarov-Treil-Volberg, to reduce the matter to checking a certain carleson measure condition. This condition is checked with a corona decomposition of the weight. Prior proofs of this type have used Bellman functions, while this proof is flexible enough to address all Haar shifts at the same time.
Original languageEnglish
Pages (from-to)127
JournalMathematische Annalen
Publication statusPublished - 10 Jun 2009

Bibliographical note

14 pages, submitted to math annalen. Typos corrected. This is the final version of the paper


  • math.CA
  • 42


Dive into the research topics of 'Sharp A 2 inequality for Haar shift operators'. Together they form a unique fingerprint.

Cite this