Small cap decoupling inequalities: Bilinear methods
Changkeun Oh
TL;DR
This paper establishes sharp small cap decoupling inequalities for the moment curve in higher dimensions using bilinear methods, extending previous results to a broader range of exponents and dimensions.
Contribution
It generalizes existing decoupling inequalities to higher dimensions with a bilinear approach, broadening the scope of applicable exponents.
Findings
Sharp decoupling inequalities for the moment curve
Extension to higher dimensions
Generalization of previous results
Abstract
We obtain sharp small cap decoupling inequalities associated to the moment curve for certain range of exponents . Our method is based on the bilinearization argument due to Bourgain and Bourgain-Demeter. Our result generalizes theirs to all higher dimensions.
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