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Investigation demonstrates L^p estimates for multilinear multipliers, indicating rank impacts on bounds.
We establish Lᵖ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on Rᵈ. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension m. The difficulty of proving Lᵖ bounds increases with the rank m/d, and our focus is on the fractional rank case m/d<n/2≤ m/d.
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Jianghao Zhang (2025) studied this question.
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