A Stein-Tomas type estimate and a decoupling inequality
Xiaochun Li
TL;DR
This paper establishes a Stein-Tomas type inequality and a weak decoupling inequality using polynomial partitioning, linking these results to Waring's problem in number theory.
Contribution
It introduces new inequalities derived via polynomial partitioning, connecting harmonic analysis techniques to classical number theory problems.
Findings
Proved a Stein-Tomas type inequality.
Established a weak decoupling inequality.
Linked inequalities to Waring's problem.
Abstract
A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials · Spectral Theory in Mathematical Physics