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

Krause, Ben and Mirek, Mariusz and Trojan, Bartosz (2018) Two-parameter version of Bourgain's inequality: Rational frequencies. Advances in Mathematics, 323 . pp. 720-744. ISSN 0001-8708.

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Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on L^2(R^2) 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.

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Additional Information:© 2017 Elsevier Inc. Received 18 February 2016, Accepted 21 October 2017, Available online 14 November 2017. 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.
Funding AgencyGrant Number
Schmidt Science FellowsUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
National Science Centre (Poland)DEC-2015/19/B/ST1/01149
Subject Keywords:Multi-parameter maximal functions; Littlewood–Paley theory; Oscillation semi-norms
Record Number:CaltechAUTHORS:20171115-092851387
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Official Citation:Ben Krause, Mariusz Mirek, Bartosz Trojan, Two-parameter version of Bourgain's inequality: Rational frequencies, Advances in Mathematics, Volume 323, 7 January 2018, Pages 720-744, ISSN 0001-8708, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83216
Deposited By: Tony Diaz
Deposited On:15 Nov 2017 19:34
Last Modified:15 Nov 2017 19:34

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