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.
All Science Journal Classification (ASJC) codes
- Littlewood–Paley theory
- Multi-parameter maximal functions
- Oscillation semi-norms