ℓ^p improving estimates are derived for multilinear forms from all distance graphs with 2, 3, or 4 vertices and from chains and simplexes of arbitrary size in Z^d, with some bounds depending only on vertex count rather than graph structure.
The VC-dimension and point config- urations inR d
2 Pith papers cite this work. Polarity classification is still indexing.
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Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.
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$\ell^{p}$ improving estimates for multilinear forms motivated by distance graphs
ℓ^p improving estimates are derived for multilinear forms from all distance graphs with 2, 3, or 4 vertices and from chains and simplexes of arbitrary size in Z^d, with some bounds depending only on vertex count rather than graph structure.
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Joint upper Banach density, VC dimensions and Euclidean point configurations
Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.