Two-parameter version of Bourgain's inequality: Rational frequencies
Copyright policy )Two-parameter version of Bourgain's inequality: Rational frequencies
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.
17 pages, no figures
- California Institute of Technology United States
- Institute for Advanced Study United States
- Polish Academy of Learning Poland
- University of Wrocław Poland
- Mississippi School for Mathematics and Science United States
Maximal functions, Littlewood-Paley theory, oscillation semi-norms, Oscillation semi-norms, \(H^p\)-spaces, 510, Functional Analysis (math.FA), Littlewood-Paley theory, Mathematics - Functional Analysis, Littlewood–Paley theory, Mathematics - Classical Analysis and ODEs, Multi-parameter maximal functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, multi-parameter maximal functions
Maximal functions, Littlewood-Paley theory, oscillation semi-norms, Oscillation semi-norms, \(H^p\)-spaces, 510, Functional Analysis (math.FA), Littlewood-Paley theory, Mathematics - Functional Analysis, Littlewood–Paley theory, Mathematics - Classical Analysis and ODEs, Multi-parameter maximal functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, multi-parameter maximal functions
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