Two-parameter Version of Bourgain's Inequality: Rational Frequencies

Ben Krause; Mariusz Mirek; Bartosz Trojan

doi:10.1016/j.aim.2017.10.033

Two-parameter Version of Bourgain's Inequality: Rational Frequencies

Ben Krause, Mariusz Mirek, Bartosz Trojan

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	720-744
Journal	ADVANCES IN MATHEMATICS
Volume	323
Issue number	7
Early online date	7 Jan 2018
DOIs	https://doi.org/10.1016/j.aim.2017.10.033
Publication status	E-pub ahead of print - 7 Jan 2018

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10.1016/j.aim.2017.10.033

Cite this

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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.",

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AB - 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.

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