Two-parameter version of Bourgain's inequality: Rational frequencies

Ben Krause, Mariusz Mirek, Bartosz Trojan

Research output: Contribution to journalArticlepeer-review


Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on L2(R2) for the rational frequencies. We achieve this by introducing a variant of a two-parameter Rademacher–Menschov inequality. The method allows us to control an oscillation seminorm as well.

Original languageEnglish (US)
Pages (from-to)720-744
Number of pages25
JournalAdvances in Mathematics
StatePublished - Jan 7 2018
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


  • Littlewood–Paley theory
  • Multi-parameter maximal functions
  • Oscillation semi-norms


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