English

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

Classical Analysis and ODEs 2015-04-17 v1 Functional Analysis

Abstract

Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on L2(R2)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.

Keywords

Cite

@article{arxiv.1504.04132,
  title  = {Two-parameter version of Bourgain's inequality: Rational frequencies},
  author = {Ben Krause and Mariusz Mirek and Bartosz Trojan},
  journal= {arXiv preprint arXiv:1504.04132},
  year   = {2015}
}

Comments

17 pages, no figures

R2 v1 2026-06-22T09:17:02.401Z