The paper derives ℓ^p improving estimates for multilinear forms Λ_G associated to distance graphs on Z^d with 2-4 vertices as well as arbitrary chains and simplexes, finding that some properties depend only on vertex count.
Finite chains inside thin subsets ofR d.Anal
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$\ell^{p}$ improving estimates for multilinear forms motivated by distance graphs
The paper derives ℓ^p improving estimates for multilinear forms Λ_G associated to distance graphs on Z^d with 2-4 vertices as well as arbitrary chains and simplexes, finding that some properties depend only on vertex count.