This paper proves the restriction conjecture implies the decoupling theorem for hyperbolic paraboloids, highlighting its implications for l^p spaces.
In this short paper, we prove that the restriction conjecture for the (hyperbolic) paraboloid in Rᵈ implies the lᵖ -decoupling theorem for the (hyperbolic) paraboloid in R²ᵈ⁻¹ . In particular, this gives a simple proof of the lᵖ decoupling theorem for the (hyperbolic) paraboloid in R³ .
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Changkeun Oh (2025) studied this question.
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