Establishes L² oscillation inequality for polynomial averages in function fields, implying a.e. pointwise convergence and L² maximal bound.
To appear in theProceedings of the International Congress of Mathematicians
2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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Extends Ionescu-Wainger multiplier theorem to weighted and seminorm settings with non-uniform bounds and applies it to Bourgain's polynomial ergodic theorem.
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Bourgain's $L^2$ pointwise ergodic theorem over function fields
Establishes L² oscillation inequality for polynomial averages in function fields, implying a.e. pointwise convergence and L² maximal bound.