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arXiv · 1504.04132

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

Ben Krause·Mariusz Mirek·Bartosz Trojan
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Abstract

Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on $L^2(\mathbb R^2)$ 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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Ben Krause, Mariusz Mirek, Bartosz Trojan. 2015-04-16. Two-parameter version of Bourgain's inequality: Rational frequencies. https://arxiv.org/abs/1504.04132

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