@article{d67dc9df1c3f4ae08f5ce6050bcedc87,
title = "Two-parameter version of Bourgain's inequality: Rational frequencies",
abstract = "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.",
keywords = "Littlewood–Paley theory, Multi-parameter maximal functions, Oscillation semi-norms",
author = "Ben Krause and Mariusz Mirek and Bartosz Trojan",
note = "Funding Information: The authors thank the Hausdorff Research Institute for Mathematics in Bonn for support and hospitality during the Trimester Program “Harmonic Analysis and Partial Differential Equation”. Mariusz Mirek was partially supported by the Schmidt Fellowship and the IAS Found. for Math. and by the National Science Center, NCN grant DEC-2015/19/B/ST1/01149 . Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",
year = "2018",
month = jan,
day = "7",
doi = "https://doi.org/10.1016/j.aim.2017.10.033",
language = "English (US)",
volume = "323",
pages = "720--744",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}