Improved Cotlar's inequality in the context of local Tb theorems

Henri Martikainen, Mihalis Mourgoglou, Xavier Tolsa

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1 Citation (Scopus)

Abstract

© 2018 Elsevier Inc. In the context of local Tb theorems with Lp testing conditions we prove an enhanced Cotlar's inequality. This is related to the problem of removing the so called buffer assumption of Hytönen–Nazarov, which is the final barrier for the full solution of S. Hofmann's problem. We also investigate the problem of extending the Hytönen–Nazarov result to non-homogeneous measures. We work not just with the Lebesgue measure but with measures μ in Rd satisfying μ(B(x,r))≤Crn, n∈(0,d]. The range of exponents in the Cotlar type inequality depend on n. Without assuming buffer we get the full range of exponents p,q∈(1,2] for measures with n≤1, and in general we get p,q∈[2−ϵ(n),2], ϵ(n)>0. Consequences for (non-homogeneous) local Tb theorems are discussed.
Original languageEnglish
Pages (from-to)1255-1275
JournalJournal of Functional Analysis
Volume274
Issue number5
DOIs
Publication statusPublished - 1 Mar 2018

Keywords

  • Cotlar's inequality
  • Local Tb theorems
  • Non-homogeneous analysis

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